Special right triangles how do you solve them

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

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

24

step-by-step explanation:

the graph shows 30% of students walk. 80 students were questioned, so the number that said they walk is

30% × 80 = 0.30 × 80 = 24

the furthest the dog can be is 508 meters away from the house, and the closest he can be is 492 meters away from the house.