Question

1. find each of the indicated sides.

(image of a right triangle with a smaller similar right triangle inside, angle 28°, base 6.3 m, top segment 0.8 m, hypotenuse x, height y)

Explanation:

Step1: Calculate adjacent side length

Adjacent side = 6.3 - 0.8 = 5.5 m

Step2: Find x using cosine

$\cos(28^\circ) = \frac{5.5}{x} \Rightarrow x = \frac{5.5}{\cos(28^\circ)}$
$x \approx \frac{5.5}{0.8829} \approx 6.23$ m

Step3: Find y using tangent

$\tan(28^\circ) = \frac{y}{5.5} \Rightarrow y = 5.5 \times \tan(28^\circ)$
$y \approx 5.5 \times 0.5317 \approx 2.92$ m

Answer:

$x \approx 6.23$ m, $y \approx 2.92$ m