Question

The measures of the sides of ΔPQR are given in the diagram. What is m∠P, correct to two decimal places? what would the formula?

Answer 1

please you have to compute the area of your triangle first

Answer 2

bxh/2

Answer 3

in order to that, you can apply the formula of Erone, namely:
\[A = \sqrt {p\left( {p - a} \right)\left( {p - b} \right)\left( {p - c} \right)} \]
where p is the half-perimeter, and a, b, c are the sides

Answer 4

hint:
\[p = \frac{{a + b + c}}{2}\]\[p = \frac{{a + b + c}}{2}\]

Answer 5

ok trying to calculate but calculator died :(

Answer 6

try to use Windows calc.

Answer 7

true

Answer 8

got 7.375

Answer 9

that is the half-perimeter

Answer 10

so multiply?

Answer 11

14.75

Answer 12

hint:
what is:
\[A = \sqrt {7.375\left( {7.375 - 4.71} \right)\left( {7.375 - 5.79} \right)\left( {7.375 - 4.25} \right)} = ...?\]

Answer 13

ok

Answer 14

hint:
\[\begin{gathered}
A = \sqrt {7.375\left( {7.375 - 4.71} \right)\left( {7.375 - 5.79} \right)\left( {7.375 - 4.25} \right)} = \hfill \\
= \sqrt {7.375 \times 2.665 \times 1.585 \times 3.125} ...? \hfill \\
\end{gathered} \]

Answer 15

im doing it sorry put new batteries

Answer 16

you should get this:
\[A = 9.867\]
please check that result!

Answer 17

next, in order to find the requested angle, you have to apply the subsequent formula:
\[9.867 = \frac{1}{2} \times 4.25 \times 5.79 \times \sin P\]

Answer 18

please solve that formula in order to find the value of \[\sin P\]

Answer 19

more explanation, the general formula, is:
\[A = \frac{1}{2}r \cdot q \cdot \sin P\]