Question

I need help with these answers please just 3 questions that in the pictures,

1. In right triangle DEF, ∠E is a right angle, m∠D=26∘, and DF=4.5.
sin26∘≈0.44
cos26∘≈0.90
tan26∘≈0.49
Triangle D E F with measures as described in the text
What is the measurement of EF?
If necessary, round your answer to two decimal places, like this: 42.53
.
2. In right triangle ABC, ∠C is a right angle, m∠A=52∘, AC=10.01, and AB=c.
sin52∘≈0.788
cos52∘≈0.616
tan52∘≈1.280
Triangle A B C with measures as described in the text.
What is the measurement of AB?
If necessary, round your answer to two decimal places, like this: 42.53
.
3. In right triangle GHI, ∠H is a right angle, m∠I=42∘, and GH=11.
sin42∘≈0.67
cos42∘≈0.74
tan42∘≈0.90
Triangle G H I has segment G H that measures 11 units. Angle H is a right angle and angle I is 42 degrees.
What is the measurement of HI?
If necessary, round your answer to two decimal places, like this: 42.53

Answer 1

9514 1404 393

Answer:

1. EF = 1.98
2. AB = 16.25
3. HI = 12.22

Explanation:

The mnemonic SOH CAH TOA is useful for these. It reminds you of the relations between sides and trig functions in a right triangle.

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1. The side of interest is opposite the given angle. The given side is the hypotenuse.

Sin = Opposite/Hypotenuse

sin(26°) = EF/DF = EF/4.5

EF = 4.5·sin(26°) = 4.5·0.44 = 1.98 . . . units

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2. The given side is adjacent to the given angles. The desired length is that of the hypotenuse.

Cos = Adjacent/Hypotenuse

cos(52°) = AC/AB = 10.01/c

c = 10.01/cos(52°) = 10.01/0.616 ≈ 16.25 . . . units

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3. The given side is opposite the given angle, and the desired side length is adjacent to the given angle.

Tan = Opposite/Adjacent

tan(42°) = 11/HI

HI = 11/tan(42°) = 11/0.90 = 12.22 . . . units