Question

Harry is trying to calculate the height of a tower. He is standing 95 meters from the base of a tower. The angle of elevation from Harry's position on the ground and the top of the tower is 35°. Calculate the height of the tower to the nearest tenth of a meter.

A) 54.5 meters
B) 62.7 meters
C) 66.5 meters
D) 77.8 meters

Answer 1

C) 66.5 meters.

Explanation:

Please find the attachment.

We have been given that Harry is standing 95 meters from the base of a tower. The angle of elevation from Harry's position on the ground and the top of the tower is 35°.

We can see from our attachment that tower, Harry and the angle of elevation with top of tower form a right triangle.

We can see that height of tower is opposite side and distance between Harry and tower is adjacent side for our given angle of elevation.

Since tangent relates the opposite side of a right triangle with its adjacent side.

`\text{Tan}=\frac{\text{Opposite}}{\text{Adjacent}}`

Upon substituting our given values in above relation we will get,

`\text{Tan}(35^o)=\frac{\text{Height of tower}}{95}`

`0.70020753821=\frac{\text{Height of tower}}{95}`

`0.70020753821*95=\frac{\text{Height of tower}}{95}*95`

`66.51971612995=\text{Height of tower}`

`\text{Height of tower}\approx 66.5`

Therefore, the height of tower is 66.5 meters and option C is the correct choice.

Answer 2

The height of the tower is the side opposite to the angle of elevation and Harry's distance from the tower is the adjacent side. To answer the question, use the trigonometric function tangent, such that,
tan 35° = x / 95 m
The value of x from the equation is 66.52 m. Thus, the answer is letter C.