SOLUTION: In a right triangle, the length of one of the legs is 8 cm and the measure of the acute angle opposite to this leg is 50°. Find the measure of the other acute angle and the length

Question 1146878: In a right triangle, the length of one of the legs is 8 cm and the measure of the acute angle opposite to this leg is 50°. Find the measure of the other acute angle and the lengths of the other leg and the hypotenuse.
Found 4 solutions by josmiceli, ikleyn, Theo, MathTherapy:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
You can use law of sines

and, also:

-----------------------------------
b = 6.7128
c = 10.4433
The angle opposite the other leg is 40 degrees
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check:

I think error is due to rounding off
check the math & maybe get better accuracy

Answer by ikleyn(52814)   (Show Source): You can put this solution on YOUR website!
.
In a right triangle, the length of one of the legs is 8 cm and the measure of the acute angle opposite to this leg is 50°.
Find the measure of the other acute angle and the lengths of the other leg and the hypotenuse.
~~~~~~~~~~~~~~~~~~

The other acute angle is 90° - 50° = 40°. The other leg is 8*tan(40°). The hypotenuse is .

When I see the solutions of some tutors at this forum that use INADEQUATELY complicated tools for simple tasks,
I often doubt if they know the Math, at all.

When you work with right triangles, the "law of sine theorem" is irrelevant ---- the trigonometric functions perform all needed operations . . .

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
you can use the law of sines to solve this.
law of sines says a/sin(A) = b/sin(B) = c/sin(C)
let your triangle be ABC
A is the 90 degree angle.
B is the 40 degree angle.
C is the 50 degree angle.
a is the side opposite angle (A)
b is the side opposite angle (B)
c is the side opposite angle (C)
measure of side c is 8.
measure of angle (C) is 50 degrees.
since angle A is 90 degrees, then angle B has to be 180 - 90 - 50 = 40 degrees.
law of sines says a/sin(A) = c/sin(C)
c = 8 and C = 50 and A = 90
formula becomes:
a/sin(90) = 8/sin(50)
solve for a to get:
a = 8 * sin(90) / sin(50) = 10.44325831
likewise, .....
c/sin(C) = b/sin(B)
this becomes:
8/sin(50) = b/sin(40)
solve for b to get:
b = 8 * sin(40) / sin(50) = 6.712797049
this is a right triangle where:
the two legs are c and b, and he hypotenuse is a.
your leg measurements are:
c = 8
b = 6.712797049
the hypotenuse measurement is:
c = 10.44325831
in a right triangle, the sum of the square of each leg is equal to the square of the hypotenuse.
that means that 6.712797049^2 + 8^2 = 10.44325831^2
do the math and you will see that 109.0616442 = 109.0616442, confirming that the lengths of the legs and the hypotenuse are correct.
your solution is:
the other acute angle is 40 degrees.
the length of the other leg is 6.712797049
the length of the hypotenuse is 10.44325831
here's my diagram.

Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!
In a right triangle, the length of one of the legs is 8 cm and the measure of the acute angle opposite to this leg is 50°. Find the measure of the other acute angle and the lengths of the other leg and the hypotenuse.

Why do these people who claim to be tutors always, always make these problems, so, so COMPLICATED.
I would NEVER encourage anyone to ask their help in this forum, as they make it so DIFFICULT for these people who need help. Why would anyone want to use the Law of sines when
calculating sides of a RIGHT-TRIANGLE? It's just ABSURD!! What are they trying to prove? That they can complicate the lives of EVERYONE who asks for a solution to a math problem!
Here are the SIMPLE answers: Other acute angle:
Length of other leg (AB):
Length of Hypotenuse:
Now, what is SO DIFFICULT about this?
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