Answer: (B) - 43°
Explanation: Using the sine rule, we can say that sinA/BC = sinC/AB
sin(61)/45 = sin(C)/35
sin(C) = 35sin(61)/45
sin(C) ≈ 0.680259772....
C = arcsin(0.680259772...)
C = 42.8639459...
C ≈ 43°
When Peter does this, he is creating two sides of a right-angle triangle. The distance from his house to that point will be the hypotenuse of the triangle thus, to work out the length of the hypotenuse, we have to use Pythagoras Theorem! So:
a² + b² = c²
15² + 15² = c²
225 + 225 = c²
450 = c²
15√2 = c
21.21320344 = c
So, this rounded to the nearest tenth would be:
21.2 meters !
Step-by-step explanation:
every triangle inscribed into a circle with the baseline being a diameter of the circle must be a right-angled triangle.
therefore,
angle XVY = 90°.
for VY we can use Pythagoras
c² = a² + b²
with c being the Hypotenuse (the line opposite of the 90° angle, in our case XY).
XY = 2×ZY = 2×17 = 34.
so,
34² = 30² + VY²
VY² = 34² - 30² = 1156 - 900 = 256
VY = 16
I think what you meant was
(2x - 5)² = 11 -- (1)
Square root both sides of (1), i.e.
√(2x - 5)² = ± √11 -- (2)
From (2), we have
2x - 5 = ± √11 -- (3)
By adding 5 to both sides in (3), we have
2x = 5 ± √11 -- (4)
Divide both sides of (4) by 2, and we obtain
x = (5 ± √11)/2 -- (5)
From (5), the solution set of (1) is
x = (5 + √11)/2, (5 - √11)/2 ...Ans.
