Math / Trigonometry

Question $\text { - }\left.\right|^{h=}$ $c=$

Studdy Solution

STEP 1

1. The first triangle is a 30°-60°-90° right triangle.
2. The second triangle is a 45°-45°-90° right triangle.
3. We need to find the lengths of $h$ and $c$ .

STEP 2

1. Solve for $h$ in the 30°-60°-90° triangle.
2. Solve for $c$ in the 45°-45°-90° triangle.

STEP 3

Recall the properties of a 30°-60°-90° triangle: - The side opposite the 30° angle is half the hypotenuse. - The side opposite the 60° angle is $\sqrt{3}$ times the side opposite the 30° angle.
Given that the hypotenuse is 8, calculate $h$ :
$h = \frac{1}{2} \times 8 = 4$

STEP 4

Recall the properties of a 45°-45°-90° triangle: - The legs are equal. - The hypotenuse is $\sqrt{2}$ times the length of each leg.
Given that one leg is 2, calculate $c$ :
$c = 2$
The lengths are:
$h = \boxed{4}$ $c = \boxed{2}$

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