Mathematics: what is y in degree’s rounded to the nearest tenth?

what is y in degree’s rounded to the nearest, №13638535, 14.12.2020 13:58

Mathematics

Grace is standing 14 feet from a lighthouse and kelly is standing 12 feet from grace. the angle that grace looks up to see the top of the lighthouse is 45°. the angle that kelly looks up to see the top of the lighthouse is y°. a.) find the height, h, of the lighthouse. b.) find the angle, rounded to the nearest tenth of a degree, in which kelly looks up to the top of the lighthouse. c.) to the nearest tenth of a degree, find the value of x° . in two or more sentences, explain your calculations

Step-by-step answer

P Answered by PhD

20

To find the height of the lighthouse, use $tan45= \frac{h}{14}$ to get that h = 14 (the tangent of 45 is 1). Now for the next question, you have to use the height you just solved for to find angle y. Use $tan(y)= \frac{14}{26}$ and the inverse tangent button on your calculator tells us that the angle is 28.3. Now for the last question, use the supplement of 45 to get that the angle adjacent to y is 135. 180 - 135 - 28.3 = 16.7 That's your x value.

Mathematics

Grace is standing 14 feet from a lighthouse and kelly is standing 12 feet from grace. the angle that grace looks up to see the top of the lighthouse is 45°. the angle that kelly looks up to see the top of the lighthouse is y°. find the height, h, of the lighthouse. find the angle, rounded to the nearest tenth of a degree, in which kelly looks up to the top of the lighthouse. to the nearest tenth of a degree, find the value of x° . in two or more sentences, explain your calculations

Step-by-step answer

P Answered by PhD

33

Grace has a 45 degree upwards angle, then the height of the lighthouse is 14'.

Case A. Kelly is 26 feet from the lighthouse.
The arcTangent of 14/26 is a 28.3 degree angle.

Case B. But if Kelly stood closer to the lighthouse, i.e. 2 feet away, then her angle is arcTangent of 14/2 = 81.9 degrees

Mathematics

Pls 1. a) given the provided angle and the leg provided, what trigonometric ratio is used to find the hypotenuse? write out the equation using the ratio and angle. b) what is the length of eg rounded to the nearest hundredth? include units. c) what is the measure, in degrees, of angle e? d) what is length of ef rounded to the nearest hundredth? include units. e) what is the area of triangle efg? include units. 2.a regular hexagon has an edge length of 4 cm. what is the exact area of the hexagon? do not answer with a decimal. hint: draw a picture,

Step-by-step answer

P Answered by Master

1

A) The hypotenuse is the longest side of the triangle .In the figure EG is the hypotenuse.The given angle is <G=40 degrees.The side adjacent is FG= 10 units.

The question is asking us to find the trigonometry ratio which will help us find EG.We can use cos as cos is ratio of adjacent and hypotenuse.

$cos 40=\frac{10}{Hypotenuse EG.}$

B) Cos 40 =0.766.

Substituting tan40 value we have:

$0.766=\frac{10}{EG}$

EG=13.05.

C)Sum of angles in triangle is 180.

<E+<F+<G=180

<E+90+40=180

<E+130=180

<E=50 degrees.

D) $Tan 40=\frac{EF}{10}$

EF=8.39

E) Area of triangle EFG= $\frac{1}{2}x base x height.$

A rea of the triangle = $\frac{1}{2}x8.39x13.05$

Area= 54.75 square units.

Mathematics

Pls 1. a) given the provided angle and the leg provided, what trigonometric ratio is used to find the hypotenuse? write out the equation using the ratio and angle. b) what is the length of eg rounded to the nearest hundredth? include units. c) what is the measure, in degrees, of angle e? d) what is length of ef rounded to the nearest hundredth? include units. e) what is the area of triangle efg? include units. 2.a regular hexagon has an edge length of 4 cm. what is the exact area of the hexagon? do not answer with a decimal. hint: draw a picture,

Step-by-step answer

P Answered by Specialist

1

A) The hypotenuse is the longest side of the triangle .In the figure EG is the hypotenuse.The given angle is <G=40 degrees.The side adjacent is FG= 10 units.

The question is asking us to find the trigonometry ratio which will help us find EG.We can use cos as cos is ratio of adjacent and hypotenuse.

$cos 40=\frac{10}{Hypotenuse EG.}$

B) Cos 40 =0.766.

Substituting tan40 value we have:

$0.766=\frac{10}{EG}$

EG=13.05.

C)Sum of angles in triangle is 180.

<E+<F+<G=180

<E+90+40=180

<E+130=180

<E=50 degrees.

D) $Tan 40=\frac{EF}{10}$

EF=8.39

E) Area of triangle EFG= $\frac{1}{2}x base x height.$

A rea of the triangle = $\frac{1}{2}x8.39x13.05$

Area= 54.75 square units.

Mathematics

Find the lengths of the missing sides in the triangle. Write your answers as integers or as decimals rounded to the nearest tenth. The diagram is not drawn to scale. A right triangle is shown with an angle that measures 45 degrees. The side opposite of the 45 degree angle is 7. The side opposite of the unlabeled angle is y. The side opposite of the right angle is x.

Step-by-step answer

P Answered by Master

Length of y = 7 units

Length of x = 9.9 units

Step-by-step explanation:

From the trigonometric ratios we know

$\tan\theta=\dfrac{\text{Perpendicular}}{\text{Base}}\\\Rightarrow \tan45^{\circ}=\dfrac{7}{y}\\\Rightarrow y=\dfrac{7}{\tan45^{\circ}}\\\Rightarrow y=7$ $\tan45^{\circ}=1$

Length of y = 7 units

From Pythagoras theorem

$x=\sqrt{7^2+y^2}\\\Rightarrow x=\sqrt{7^2+7^2}\\\Rightarrow x=7\sqrt{2}=9.9\ \text{units}$

Length of x = 9.9 units

Mathematics

Find the lengths of the missing sides in the triangle. Write your answers as integers or as decimals rounded to the nearest tenth. The diagram is not drawn to scale. A right triangle is shown with an angle that measures 45 degrees. The side opposite of the 45 degree angle is 7. The side opposite of the unlabeled angle is y. The side opposite of the right angle is x.

Step-by-step answer

P Answered by Specialist

Length of y = 7 units

Length of x = 9.9 units

Step-by-step explanation:

From the trigonometric ratios we know

$\tan\theta=\dfrac{\text{Perpendicular}}{\text{Base}}\\\Rightarrow \tan45^{\circ}=\dfrac{7}{y}\\\Rightarrow y=\dfrac{7}{\tan45^{\circ}}\\\Rightarrow y=7$ $\tan45^{\circ}=1$

Length of y = 7 units

From Pythagoras theorem

$x=\sqrt{7^2+y^2}\\\Rightarrow x=\sqrt{7^2+7^2}\\\Rightarrow x=7\sqrt{2}=9.9\ \text{units}$

Length of x = 9.9 units

Mathematics

Triangle X Y Z is shown. Angle X Y Z is 51 degrees and angle Y Z X is 76 degrees. The length of X Z is 2.6, the length of X Y is z, and Y Z is x. Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction What is the value of z, rounded to the nearest tenth? Use the law of sines to find the answer. 2.7 units 3.2 units 4.5 units 5.3 units

Step-by-step answer

P Answered by PhD

10

$z=3.2\ units$