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Find the lengths of the other two sides of a right triangle if the length of the hypotenuse is 8 inches and one of the angles is 30°. 
  • a)
     4, 4√3 inches
  • b)
    5, 6 inches
  • c)
    2, 4√2
  • d)
    3, 4√2 inches
  • e)
    None of these
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Find the lengths of the other two sides of a right triangle if the len...
This is a right triangle with a 30° angle so it must be a 30°-60°-90° triangle.
You are given that the hypotenuse is 8. Substituting 8 into the third value of the ratio n: n√3 :2n,
we get that 2n = 8 n = 4
Substituting n = 4 into the first and second value of the ratio we get that the other two sides are 4 and 4√3
The lengths of the two sides are 4 inches and 4√3 inches.
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Most Upvoted Answer
Find the lengths of the other two sides of a right triangle if the len...
To solve this problem, we can use trigonometric functions, specifically the sine and cosine functions.

Let's denote the length of one of the other two sides of the right triangle as 'x'. Since one of the angles is 30 degrees, we can use the trigonometric ratios of a 30-60-90 triangle to find the value of 'x'.

In a 30-60-90 triangle, the ratio of the lengths of the sides opposite the angles are as follows:
- The side opposite the 30 degree angle is x.
- The side opposite the 60 degree angle is x√3.
- The hypotenuse is 2x.

So, in our given right triangle, we know that the hypotenuse is 8 inches. Using the above ratios, we can set up the following equation:

2x = 8

Solving for 'x', we find that x = 4 inches.

Therefore, the lengths of the other two sides of the right triangle are 4 inches and 4√3 inches.

So, the correct answer is option A: 4, 4√3 inches.
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Find the lengths of the other two sides of a right triangle if the length of the hypotenuse is 8 inches and one of the angles is 30.a)4, 43 inchesb)5, 6 inchesc)2, 42d)3, 42 inchese)None of theseCorrect answer is option 'A'. Can you explain this answer?
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