Question

You are measuring the height of a statue. You stand 10 feet from the base of the statue. You measure the angle of elevation from the ground to the top of the statue to be 76 degrees find the height h of the statue to the nearest foot

Answer 1

Answer:

h = (10 ft)(4.01) = 40.1 ft

Step-by-step explanation:

The tangent function relates this elevation to the horizontal distance (10 ft) and the angle of elevation (76 degrees):

                               opp           h

tan 76 degrees = --------- = ------------- = 4.01

                                adj         10 ft

Therefore , h = (10 ft)(4.01) = 40.1 ft

Answer 2

Answer: 40 ft

Step-by-step explanation:

You can find the height of the statue by solving the right triangle.

In this case the adjacent side of the triangle is the horizontal distance to the statue (10 ft). The height of the statue is the opposite side to the angle of 76 °.

By definition, the tangent of an angle is:

$tan(\theta) = \frac{opposite}{adjacent}$

In this case

$\theta=76\°\\\\opposite = h\\\\adjacent = 10\ ft$

Therefore

$tan(76) = \frac{h}{10}$

$h=tan(76) * 10\\\\h=40\ ft$