Tell whether it is possible to draw a triangle with the given side lengths.
1 answer:
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One of the numbers is 40 and the other one is 63
confirmation:
63×(2/3)-2=40
and 40+63=103
confirmation:
63×(2/3)-2=40
and 40+63=103
Since S is a point on the segment QR, then:
Use the diagram and trigonometric relationships to find the value of QS and QR. Then, use the above equation to solve for SR.
In the right triangle PQS, the side QS is opposite to the angle of 32º, and the side PQ is adjacent to the angle of 32º. Then, use the tangent trigonometric function to relate PQ to QS:
Isolate QS and replace PQ=14:
On the other hand, notice that the side QR in the right triangle PQR is opposite to the angle QPR, which has a measure of 32º+24º=56º.
Then, by a similar reasoning, we can use again the tangent function to find QR:
We have found expressions for QS and QR in terms of trigonometric relationships. Then, we can find an expression for SR:
Replace the expressions for QR and QS:
Use a calculator to find decimal expressions for tan(56º) and tan(32º). Then, find SR:
Therefore, to the nearest tenth, the length of the side SR (or RS, which is the same) is 12.0.