The altitude from P to the side QR will be 8 inches. The concept of trigonometry is used in the given problem.
What is trigonometry?
The field of mathematics is concerned with the relationships between triangles' sides and angles, as well as the related functions of any angle.
The given data in the problem is;
PQ = 17 in
PR = 10 in
QR = 21 in
h is the altitude
The perimeter of the triangle is;
[tex]\rm s = \frac{17+10+21}{2} \\\\ s=24[/tex]
The area of the triangle is found as;
[tex]\rm A = \sqrt{S(S-PR)(S-PQ)(S-QR)} \\\\ \rm A = \sqrt{24(24-17)(24-10)(24-21)} \\\\ A=\sqrt{24 \times 7 \times 3 \times 14} \\\\ A=84 \ inch[/tex]
From the graph the area of ta triangle is;
[tex]\rm A = \frac{1}{2} \times b \times h \\\\ 84=\frac{1}{2} \times 21 \times h \\\\ h=\frac{2 \times 84}{21} \\\\ h= 8 \ inch[/tex]
Hence the altitude from P to the side QR will be 8 inches.
To learn more about the trigonometry refer to the link;
https://brainly.com/question/26719838
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