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Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form. x= y=

Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers-example-1
User Vedarthk
by
8.2k points

1 Answer

5 votes

Answer:

x = 10 units, y = 5 units

Explanation:

Given triangle ABC is a 30-60-90 triangle,

m∠C = 60°

By applying Sine rule in the given triangle,

Sin(60)°=
\frac{\text{Opposite side}}{\text{Hypotenuse}}

Sin(60)°
=\frac{\text{AB}}{\text{AC}}


(√(3))/(2)=\frac{\text{AB}}{\text{AC}}


(√(3))/(2)=(5√(3))/(x)

x = 10 units

Similarly, by applying Cosine rule in the given triangle,

Cos(60)° =
\frac{\text{Adjacent side}}{\text{Hypotenuse}}

Cos(60)° =
=\frac{\text{BC}}{\text{AC}}


(1)/(2)=(y)/(x)

y =
(x)/(2)

y = 5 units

Therefore, x = 10 units and y = 5 units will be the answer.

Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers-example-1
User MK Singh
by
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