Question

A 133-foot antenna is on top of a tall building. From a point on the ground, the angle of elevation to the top of the antenna is 30.5°, while the angle of elevation to the bottom of the antenna from the same point is 21.5°. How tall is the building? (Round your answer to the nearest whole number.)

Answer 1

Answer:

Explanation:

<ADC = 30.5 Degree

<BDC = 21.5 Degree

AB = 133 ft

$in \Delta BCD$

$tan 21.5= \frac{BC}{CD}$

$CD = \frac{BC}{tan21.5}$

in$\Delta ACD$

$tan 30.5 =\frac{AC}{CD}$

$CD = \frac{AB+BC}{tan30.5}$

$\frac{BC}{tan21.5} = \frac{AB}{tan30.5} +\frac{BC}{tan30.5}$

$\frac{BC}{tan21.5} - \frac{BC}{tan30.5} = 225.78$

2.5BC - 1.69BC = 225.78

BC = 281.40 ft