Question

question 1 (mandatory) (1 point) saved
frank wants to know the height of a sign across a road. he stands directly across from the sign and notices the angle of elevation to the top of the sign is 19°. frank then walks 20 m parallel to the road and observes the angle between the base of the sign and franks previous spot is 52°. what is the height, h, of the sign to the nearest tenth of a metre?
a) 12.6 m
b) 9.5 m
c) 8.8 m
d) 11.0 m
question 2 (mandatory) (1 point) saved

Explanation:

Step1: Find the distance from Frank's first position to the sign

Let the distance from Frank's first position to the sign be \(x\).
We know that \(\tan(52^{\circ})=\frac{20}{x}\), so \(x = \frac{20}{\tan(52^{\circ})}\).
Using a calculator, \(\tan(52^{\circ})\approx1.2799\), then \(x=\frac{20}{1.2799}\approx15.63\) m.

Step2: Calculate the height of the sign

We know that \(\tan(19^{\circ})=\frac{h}{x}\).
Since \(x\approx15.63\) m, then \(h=x\times\tan(19^{\circ})\).
Using a calculator, \(\tan(19^{\circ})\approx0.3443\), so \(h = 15.63\times0.3443\approx9.5\) m.

Answer:

B. 9.5 m