Question

Find PQ, if AB =150m, angle p=30° and angle Q=45°

Answer 1

PQ = 409.8

To find : The value of PQ.

Given :  

AB = 150 m   ;   ∠p = 30°   ;   ∠Q = 45°

From the figure,

In ΔAPB,

   tan P = $\frac{opposite\\\\\\\\\\\\side}{adjacent \\\\side}$

   tan P = $\frac{AB}{PB}$

   tan 30° = $\frac{AB}{PB}$

        $\frac{1}{\sqrt{3} }$  $= \frac{150}{PB}$

        PB = 150 × $\sqrt{3}$

In ΔABQ,

   tan Q = $\frac{AB}{BQ}$

   tan 45° =  $\frac{AB}{BQ}$

            1 = $\frac{150}{BQ}$

        BQ = 1 × 150

Thus, PQ = PB + BQ

               =  150 × $\sqrt{3}$ + 1 × 150

               = 150( $\sqrt{3}$ + 1 )

               = 150 × ( 1.732+1)

               = 150 × 2.732

         PQ = 409.8

Therefore, the value of PQ is 409.8.

To learn more...

brainly.in/question/1024834

Answer 2

Answer:

In triangle ABQ

tan 45°= AB/BQ

1=150/BQ

BQ=150 m

In triangle ABP

tan 30°=AB/PB

1/root 3 =150/PB

PB=150root 3=150×1.732=259.8

PQ=PB+BQ

PQ=(259.8+150)m

PQ=409.8 m ANS