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saul85 [17]
3 years ago
12

The acute angles of a right triangle are in the ratio of 7:11. Find the measure of each angle.

Mathematics
2 answers:
kondor19780726 [428]3 years ago
4 0

Answer:

B

Step-by-step explanation:

Since it's a right angle triangle, one angle has to be 90.

Total angle in a triangle = 180

Other two should add up to 90.

7/18 × 90 = 35

11/18 × 90 = 55

Tbe angles are 35°, 55° and 90°

nalin [4]3 years ago
4 0

Step-by-step explanation:

Let the common multiplier of the given ratios be x.

Therefore measures of acute angles will be 7x and 11x.

\therefore \: 90 \degree + 7x + 11x = 180 \degree \\  \\  \therefore \:  18x = 180 \degree - 90 \degree \\  \\ \therefore \:  18x = 90 \degree \\  \\ \therefore \:  x =  \frac{90 \degree }{18}  \\  \\  \therefore \:  x =  5\degree  \\  \\ \therefore \: 7x = 7 \times 5\degree  = 35\degree  \\ \& \: 11x = 11 \times 5\degree  = 55\degree

Hence, measure of each angle of right triangle are 35°, 55°, 90°.

Thus, option B is the correct answer.

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What two numbers multiply to 54 and add up to 7
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Xy = 54
x + y = 7

xy = 54
\frac{xy}{x} = \frac{54}{x}
y = \frac{54}{x}

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x = \frac{7 \± \sqrt{-167}}{2}
x = \frac{7 \± i\sqrt{167}}{2}
x = \frac{7 \± 12.9i}{2}
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x = 3.5 + 6.45i    or    3.5 - 6.45i

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- (3.5 + 6.45i)       - (3.5 + 6.45i)
                        y = 3.5 - 6.45i
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- (3.5 - 6.45i)     - (3.5 - 6.45i)
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The two numbers that add up to 7 and can multiply to 54 is 3.5 ± 6.45i.
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