Solve the right triangle ABC with right angle C, if B=30 degrees, and C = 10
1 answer:
Answer:
The answer to your question is letter D
Step-by-step explanation:
We know that the sum of the internal angles in a triangle equals 180°.
So, B = 30°, C = 90° and A = ?
A + B + C = 180°
Substitution
A + 30 + 90 = 180
Solve for A
A = 180 - 30 - 90
A = 180 - 120
A = 60°
To find "b". use the trigonometric function sine
sin B =
sin B x hypotenuse = Opposite side
Opposite side = sin 30 x 10
Opposite side = 0.5 x 10
Opposite side = b = 5.0
To find "a" use the trigonometric function cosine
Cos A = adjacent side / hypotenuse
Adjacent side = a = cos A x hypotenuse
Adjacent side = a = cos 60 x 10
a = 0.866 x 10
a = 8.66
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Answer:
156.06 ft²
Step-by-step explanation:
The applicable formula for the area of the triangle is ...
Area = (1/2)bc·sin(A)
Filling in the given numbers, you have ...
Area = (1/2)(30 ft)(14 ft)·sin(48°) ≈ 156.06041335 ft²
The area of the triangle is about 156.06 square feet.
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Sufficient digits are provided here so that you can round to the precision you (or your computer) may desire.
