Question

Can help me for this question for topi application of trigonometry?

Answer 1

In this question, you need to apply Heron's formula

`\begin{gathered} A=\sqrt[]{(S\cdot(S-PQ)\cdot(S-QR)\cdot(S-PR))} \\ \end{gathered}`

Where S is the semi perimeter

`\begin{gathered} S=(PQ+QR+PR)/(2) \\ \end{gathered}`

Therefore

`\begin{gathered} S=(PQ+QR+PR)/(2) \\ S=(7.3+9.6+14.7)/(2) \\ S=(31.6)/(2) \\ S=15.8 \end{gathered}`
`\begin{gathered} A=\sqrt[]{(S\cdot(S-PQ)\cdot(S-QR)\cdot(S-PR))} \\ A=\sqrt[]{(15.8\cdot(15.8-7.3)\cdot(15.8-9.6)\cdot(15.8-14.7))} \\ A=\sqrt[]{(15.8\cdot8.5\cdot6.2\cdot1.1)} \\ A=√(915.926) \\ A=30.264\text{ }cm^(2) \end{gathered}`

Now, let's calculate the requested height from

`\begin{gathered} \text{Area}=(b\cdot h)/(2) \\ \text{30.264}=(9.6\cdot h)/(2) \\ h=(30.264\cdot\:2)/(9.6) \\ h=(60.528)/(9.6) \\ h=6.305\text{ cm} \end{gathered}`