SOLUTION: the shortest side of a right triangle is 7cm, and one of the acute angles is 64 degrees. find the length of the hypotenuse and the length of the longer leg. round to the nearest te

Algebra ->  Triangles -> SOLUTION: the shortest side of a right triangle is 7cm, and one of the acute angles is 64 degrees. find the length of the hypotenuse and the length of the longer leg. round to the nearest te      Log On


   

Question 964311: the shortest side of a right triangle is 7cm, and one of the acute angles is 64 degrees. find the length of the hypotenuse and the length of the longer leg. round to the nearest tenth of a centimeter.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39626) About Me  (Show Source):
You can put this solution on YOUR website!
The shortest side would go opposite the smaller of the complimentary angles.

s+64+90=180
s=180-90-64
s=90-64
s=26 DEGREES

Make the drawing of this triangle and label everything.

LAW of SINES:
Using y for the longer side leg,

7%2Fsin%2826%29=y%2Fsin%2864%29

y=7%2Asin%2826%29%2Fsin%2864%29

You should be able also to use Law of Sines to find the hypotenuse, or you could use Pythagorean Theorem formula with the y you found to solve for the hypotenuse. You be able to figure out the rest of this.

Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!
the shortest side of a right triangle is 7cm, and one of the acute angles is 64 degrees. find the length of the hypotenuse and the length of the longer leg. round to the nearest tenth of a centimeter.
Since the shortest side is 7 cm, and the larger ACUTE angle is 64%5Eo, then with the hypotenuse being H, we can say that:

cos+64%5Eo+=+A%2FH

cos+64%5Eo+=+7%2FH

H+%2A+cos+64%5Eo+=+7 ------ Cross-multiplying

H, or hypotenuse = 7%2Fcos+64%5Eo, or 15.968 ≈ highlight_green%2816%29 cm

You can now use the hypotenuse (15.968 cm), the shorter leg (7 cm), and the pythagorean formula to determine longer leg.