Question

find the missing side length using the trigonometry functions( sine,cos,tan) mbf3c assignment 1) triangle with hypotenuse 10 cm, angle 60°, missing side x 2) triangle with base 20 m, angle 62°, missing side y 3) triangle with hypotenuse 17 cm, angle 25°, missing side a

Explanation:

Step1: Identify trigonometric ratio for x

In the first triangle, $x$ is opposite the $60^\circ$ angle, and the hypotenuse is 10 cm. Use sine:
$\sin(60^\circ) = \frac{x}{10}$

Step2: Solve for x

Rearrange and calculate:
$x = 10 \times \sin(60^\circ) = 10 \times \frac{\sqrt{3}}{2} = 5\sqrt{3} \approx 8.66$ cm

Step3: Identify trigonometric ratio for y

In the second triangle, the adjacent side to $62^\circ$ is 20 m, $y$ is the hypotenuse. Use cosine:
$\cos(62^\circ) = \frac{20}{y}$

Step4: Solve for y

Rearrange and calculate:
$y = \frac{20}{\cos(62^\circ)} \approx \frac{20}{0.4695} \approx 42.60$ m

Step5: Identify trigonometric ratio for a

In the third triangle, $a$ is adjacent to the $25^\circ$ angle, hypotenuse is 17 cm. Use cosine:
$\cos(25^\circ) = \frac{a}{17}$

Step6: Solve for a

Rearrange and calculate:
$a = 17 \times \cos(25^\circ) \approx 17 \times 0.9063 \approx 15.41$ cm

Answer:

1. $x \approx 8.66$ cm (or $5\sqrt{3}$ cm)
2. $y \approx 42.60$ m
3. $a \approx 15.41$ cm