Triangle YES has sides YE=32cm and YS=42cm. Angle Y has a measure of 78 degrees. What is the measure of side SE?
1 answer:
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Answer:
3a) The value of x = 56
3b) The measure of ∠ H T M = 90°
3c) The radius of the circle = 53
Step-by-step explanation:
3a) ∵ A F is a tangent to the circle O at point F
∵ Secant AH intersects circle O at point T
∴ (A F)² = (A T)(A H)
∴ 7( x + 7) = (21)² ⇒ ÷ 7
∴ x + 7 = 63
∴ x = 63 - 7 = 56
3b) ∵ HM is a diameter
∴ The measure of the arc HM = 180° ⇒ semi-circle
∵ ∠ H T M is inscribed angle subtended by the arc HM
∴ m ∠ H T M = half the measure of arc HM
∴ m ∠ H T M = 180° ÷ 2 = 90°
3c) ∵ Δ H T M is a right angle triangle at T
∴ (H M)² = (M T)² + (H T)² ⇒ Pythagorean theorem
∴ (H M)² = (90)² + (56)²
∴ (H M)² = 11236
∴ HM = = 106
∴ OM = 106 ÷ 2 = 53
∵ OM is the radius of the circle O
∴ The radius = 53
- Find the surface area when r is 8 inches and h is 8 inches.
A. 160π in²
B. 154π in²
C. 288π in²
D. 256π in² ☑
We are given –
⇢Radius of cylinder , r = 8 inches
⇢ Height of cylinder, h = 8 inches.
We are asked to find surface area of the given cylinder.
Formula to find the surface cylinder given by –
Now, Substitute given values –
- Henceforth,Option D is the correct answer.