Question

A)
A right triangle has a hypotenuse of length 15 and an angle of 50°, with a side opposite this angle oflength 9. A second right triangle also has an angle of 50°, with a hypotenuse of length 45. Determinethe length of the side opposite the 50° angle on the second triangle.
(1 point)
The side opposite the second triangle’s 50° angle has length 12.
The side opposite the second triangle’s 50° angle has length 75.
The side opposite the second triangle’s 50° angle has length 27.
The side opposite the second triangle’s 50° angle has length 3.
A)
Right triangle
has side lengths
,
, and
. A second righttriangle,
, has side lengths of
, 8, and 16. Find the ratio of the side opposite
to thehypotenuse of triangle
. Then use this ratio to identify the location of point
in the second righttriangle.
(1 point)
ABC AB = 6 BC = 6 3 – √ AC = 12
A′B′C′ 8 3 – √ ∠C
ABC C′
The ratio of the opposite side to the hypotenuse is , and point is opposite the side that has √3 .
2
C′ 8 3
–
√
The ratio of the opposite side to the hypotenuse is 1 , and point is opposite the side that has length 8.
2
C′
The ratio of the opposite side to the hypotenuse is 2 , and point is opposite the side that has length 8.
1
C′
The ratio of the opposite side to the hypotenuse is 1 , and point is opposite the side that has .
2
C′ 8 3
–
√

Answer 1

1) 27.
Reason: 9/15 = x/45 ⇒ x = 45*(9/15) = 27.

2) The ratio is 1/2, and C′ is opposite the side of length 8.
Reason: ABC is a 30-60-90 triangle (sides 6, 6√3, 12), so opposite/hypotenuse = 6/12 = 1/2. In the similar triangle A′B′C′ (sides 8, 8√3, 16) the side corresponding to 6 is 8, so C′ is opposite the side of length 8.