Question

3.) the angle of depression from the top of a television tower to a point on the ground 36.0 m from the bottom of the tower is 29.5°. find the height of the tower. section 2.5 - further applications of right triangles

Explanation:

Step1: Recall tangent - function in right - triangle

In a right - triangle formed by the tower, the horizontal distance from the bottom of the tower to the point on the ground, and the line - of - sight from the top of the tower to the point on the ground, the angle of depression is equal to the angle of elevation from the point on the ground to the top of the tower. Let the height of the tower be $h$. The horizontal distance $x = 36.0$ m and the angle of elevation $\theta=29.5^{\circ}$. The tangent of an angle in a right - triangle is defined as $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Apply the tangent formula

We know that $\tan\theta=\tan(29.5^{\circ})=\frac{h}{36.0}$. So, $h = 36.0\times\tan(29.5^{\circ})$.

Step3: Calculate the value of $h$

Using a calculator, $\tan(29.5^{\circ})\approx0.567$. Then $h = 36.0\times0.567 = 20.412\approx20.4$ m.

Answer:

$20.4$ m