Answer:
The radius of the circle P = 2√10 = 6.325
Step-by-step explanation:
∵ AB is a tangent to circle P at A
∴ (AB)² = BC × BE
∵ BC = 8 , AB = 12 , ED = 6
∵ BE = ED + DC + CB
∴ BE = 6 + CD + 8 = 14 + CD
∴ (12)² = 8 × (14 + DC) ⇒ (12)²/8 = 14 + CD ⇒ CD = (12)²/8 - 14
∴ CD = 4
Join PC and PE (radii)
In ΔBDC and ΔPDE ⇒ ∵ ∠PDC = Ф , ∴ ∠PDE = 180 - Ф
Use cos Rule:
∵ r² = (PD)² + (DC)² - 2(PD)(DC)cosФ
∴ r² = 16 + 16 - 32cosФ = 32 - 32cosФ ⇒ (1)
∵ r² = (PD)² + (DE)² - 2(PD)(DE)cos(180 - Ф) ⇒ cos(180 - Ф) = -cosФ
∴ r² = 16 + 36 + 48cosФ = 52 + 48cosФ ⇒ (2)
∵ (1) = (2)
∴ 32 - 32 cosФ = 52 + 48cosФ
∴ 32 - 52 = 48cosФ + 32cosФ
∴ -20 = 80cosФ
∴ cosФ = -20/80 = -1/4
∴ r² = 32 - 32(-1/4) = 32 + 8 = 40
∴ r = √40 = 2√10 = 6.325
Answer:
Length of the shadow of the pole is 6.93 metres
Step-by-step explanation:
Given:
Height of the pole = 4 m
The angle sun makes with the horizontal = 30 degrees
To Find:
Length of the shadow of the pole = ?
Solution:
The tangent ratio is the value received when the length of the side opposite of angle theta is divided by the length of the side adjacent to angle theta
Let x be the length of the shadow
According to the tangent ratio
On substituting the values,
x = 6.93 m
Negative. A negative number times a positive number is equal to a negative number. X multiplied by Y is a positive.
Split it into 7 triangles. Half-base of each is 2 so the distance of center to the midpoint of the base is (Pythagoras) square root of (4.62 - 22) = 4.162 triangle is this times 2, and with 7 triangles multiply also by 7 to get an approximate area of 58 sq in.
We are given a right triangle that has angles of 45°-45°-90°. This would
indicate that the triangle is an isosceles type. We can use some
trigonemetric functions to solve for the other legs. We do as follows:
sin 45 = p / 10
p = 5√2
cos 45 = q /10
q = 5√2
<span>Hope this answers the question. Have a nice day.</span>
