Question

Special right triangles how do you solve them

Answer 1

The interior angles of any triangle must add up to 180° in measure. Right angles have measure 90°, so the missing angles in both triangles here have measure 45°.

In a 45°-45°-90° triangle, the legs and hypotenuse occur in a ratio of 1 : √2. This means

(1) x = 48 √2

(2) 88 = √2 x → x = 88 / √2 = 44 √2

You could also set up trigonometric equations to solve for x in each case:

(1) cos(45°) = 48 / x → x = 48 / cos(45°) = 48 / (1 / √2) = 48 √2

(2) cos(45°) = x / 88 → x = 88 cos(45°) = 88 (1 / √2) = 44 √2

Answer 2

Explanation:

The interior angles of any triangle must add up to 180° in measure. Right angles have measure 90°, so the missing angles in both triangles here have measure 45°.

In a 45°-45°-90° triangle, the legs and hypotenuse occur in a ratio of 1 : √2. This means

(1) x = 48 √2

(2) 88 = √2 x → x = 88 / √2 = 44 √2

You could also set up trigonometric equations to solve for x in each case:

(1) cos(45°) = 48 / x → x = 48 / cos(45°) = 48 / (1 / √2) = 48 √2

(2) cos(45°) = x / 88 → x = 88 cos(45°) = 88 (1 / √2) = 44 √2