Question

question 5 (mandatory) (1 point)
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) 8.8 m
b) 11.0 m
c) 9.5 m
d) 12.6 m

Explanation:

Step1: Find the distance from the sign

Let the distance from Frank's initial position to the sign be \(x\). Using the tangent function for the \(52^{\circ}\) angle: \(\tan(52^{\circ})=\frac{20}{x}\), so \(x = \frac{20}{\tan(52^{\circ})}\).

Step2: Find the height of the sign

Using the tangent function for the \(19^{\circ}\) angle: \(\tan(19^{\circ})=\frac{h}{x}\). Substitute \(x\) from Step1: \(h=x\tan(19^{\circ})=\frac{20\tan(19^{\circ})}{\tan(52^{\circ})}\).
Calculate \(\tan(19^{\circ})\approx0.3443\), \(\tan(52^{\circ})\approx1.2799\).
\(h=\frac{20\times0.3443}{1.2799}\approx5.43\div1.2799\approx 8.8\)

Answer:

A. \(8.8\) m