Question

How would I find the hypotenuse and short leg?

Answer 1

Step-by-step explanation:

Remember , for RIGHT triangles  S-O-H-C-A-H-T-O-A

Cos 30 = Adjacent leg / Hypotenuse

            =   15 sqrt 3 / Hypot

 Hypot = (15 sqrt 3) / Cos 30

then  sin 30 = ED / Hypot      (Hypot was found in previous step)

       hypot * sin 30 = ED    

Answer 2

Answer:

DQ = 30 , DE = 15

Step-by-step explanation:

Using the cosine ratio in the right triangle to find hypotenuse DQ and the exact value

cos30° = $\frac{\sqrt{3} }{2}$ , then

cos30° = $\frac{adjacent}{hypotenuse}$ = $\frac{EQ}{DQ}$ = $\frac{15\sqrt{3} }{DQ}$ = $\frac{\sqrt{3} }{2}$ ( cross multiply )

$\sqrt{3}$ × DQ = 30$\sqrt{3}$ ( divide both sides by $\sqrt{3}$ )

DQ = 30

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Using the tangent ratio in the right triangle to find short leg DE and the exact value

tan30° = $\frac{1}{\sqrt{3} }$ , then

tan30° = $\frac{opposite}{adjacent}$ = $\frac{DE}{EQ}$ = $\frac{DE}{15\sqrt{3} }$ = $\frac{1}{\sqrt{3} }$ ( cross multiply )

$\sqrt{3}$ × DE = 15$\sqrt{3}$ ( divide both sides by $\sqrt{3}$ )

DE = 15