The base of a rectangle measures 8 feet and the altitude measures 6 feet. find to the nearest degree, the measure of the angle that the diagonal makes with the base.

Question

asked Apr 15, 2023 91.5k views

1 Answer

KRoy · Answer 1 · 2023-04-19T06:47:17+0000

The rectangle can be drawn as follows:

The angle we are to find is labelled θ.

Considering ΔDBC, we can use the Tangent Trigonometric Ratio to get the angle:

$\tan \theta=(BC)/(DC)$

Therefore, we can substitute as follows:

$\begin{gathered} \tan \theta=(6)/(8) \\ \tan \theta=0.75 \\ \theta=\tan ^(-1)0.75 \\ \theta=36.9\approx37^(\circ) \end{gathered}$

Therefore, the angle is 37°