Question

A tower casts a shadow that is 60 feet long when the angle of elevation of the sun is 65 degrees. How tall is the tower?

Answer 1

Answer: The tower is 128.67 feet tall.

Explanation:

Hi, the situation described forms a right triangle (see attachment)

So, we have to apply the next trigonometric function:

Tan (angle) = opposite / adjacent

Where the opposite side is the height of the tower (x)

Replacing with the values given:

Tan (65) = x / 60

Solving for x:

2.141406921 =x /60

2.141406921 (60) = x

128.67 = x

The tower is 128.67 feet tall.

Feel free to ask for more if needed or if you did not understand something.

Answer 2

128.67 feet

Explanation:

We would be solving this question using the Trigonometric function of tan.

Tan( of the angle of elevation) = height of the tower ÷ height of the shadow.

Angle of elevation = 65°

Height of the tower = unknown, which is designated as X

Height of the shadow = 60 feet.

Therefore,

tan 65° = X/ 60 feet

We crossmultiply

X = tan 65° × 60 feet

X = 128.67041523 feet.

Approximately, X = 128.67 feet.

Therefore, the tower is 128.67 feet tall.