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Degger [83]
3 years ago
5

Special right triangles how do you solve them

Mathematics
2 answers:
larisa86 [58]3 years ago
5 0

Step-by-step 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

Tems11 [23]3 years ago
4 0

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) <em>x</em> = 48 √2

(2) 88 = √2 <em>x</em>   →   <em>x</em> = 88 / √2 = 44 √2

You could also set up trigonometric equations to solve for <em>x</em> in each case:

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

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

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