Question

1. find x and y in the following diagrams.

a) 9.4 cm, 8.6 cm, x, 48°, y (with right - angled triangles diagram)

Explanation:

Step1: Solve for $x$ with Pythagoras

$x = \sqrt{(9.4)^2 + (8.6)^2}$
$x = \sqrt{88.36 + 73.96} = \sqrt{162.32} \approx 12.74$ cm

Step2: Solve for $y$ with cosine ratio

$\cos(48^\circ) = \frac{x}{y} \implies y = \frac{x}{\cos(48^\circ)}$
$y \approx \frac{12.74}{0.6691} \approx 19.04$ cm

Answer:

$x \approx 12.7$ cm, $y \approx 19.0$ cm (rounded to one decimal place)