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16.

tan XAB = XB/AB = 1.5/3.5 => Angle XAB = 23.19859

Note Angle XAB = Angle XAP

Triangle XAP is a right-angled triangle because it circumscribes a semicircle.

So angle XPB = 180-90-XAP = 66.8014

tan XPB = XB/BP = 1.5/BP

=> BP = 1.5/tan XPB = 0.6429

So radius of circle = 3.5+0.6429 = 4.1429

Radius = 4.1429/2 = 2.0714 #

 

17.

tan 37 = h/(20+x)

=> h = 0.7536(20 + x)

tan 52 = h/x

=> h = 1.2799x

So, 0.7536(20 + x) = 1.2799x

=> 0.5263x = 15.072

=> x = 28.6377

Therefore, h = 1.2799 x 28.6377 = 36.6533 #

 

 

1 Reply 2 Likes ✔Accepted Answer

Hi may I ask what is XAP “p”? Where is p? Thank you! 🌸

1 Reply 1 Like

Sorry. P is directly below B, on the circumference of the circle.  So BP is the small little part we need to compute in order to find the diameter of the semi circle.

1 Reply 1 Like

okk thank you :3

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