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3 years ago

in a right triangle, the leg opposite to the angle of 30 degrees is 7 in. find the lengths of the hypentenuse and the other leg

1 answer:

5 0

Answer:

Hypotenuse = 14 inches

Adjacent = 12.12 inches

Step-by-step explanation:

Using SOH, CAH TOA Method

According to SOH

Sin(theta) = Opposite/Hypotenuse
Given theta = 30°
Opposite = 7 inches

Sin30° = 7/Hypotenuse
Hypotenuse = 7/Sin30°
Hypotenuse = 7/0.5
Hypotenuse = 14 inches

The other leg will be the adjacent saying x using Pythagoras Theorem to get x
Hypotenuse^2 = Opposite^2 + Adjacent^2
14^2 = 7^2 + x^2
x^2 = 14^2 - 7^2
x^2 = 196 - 49
x^2 = 147
x = sqrt of 147
x = 12.12 inches

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