In triangle ABC, mc002-1.jpg is a right angle and mc002-2.jpg 45°
;. Find BC. If your answer is not an integer, leave it in simplest radical form. 10ft not drawn to be scale
To solve for BC, we can use the sine function. The sine of an angle in a right triangle is equal to the ratio of the length of the side opposite the angle to the length of the hypotenuse.
In this case, angle B is the right angle and angle C is 45°, so we can use the sine of angle C to find BC. Let's label the length of BC as x.
sin(C) = opposite/hypotenuse
sin(45°) = x/10ft
Using the fact that sin(45°) = √2/2, we can solve for x:
√2/2 = x/10ft
Cross-multiplying:
2x = 10ft * √2
2x = 10√2 ft
Dividing both sides by 2:
x = 5√2 ft
Therefore, the length of BC is 5√2 ft.
To find the length of BC in triangle ABC, we can use the trigonometric ratios.
Since triangle ABC has a right angle at C, we can use the properties of a right triangle to find the lengths of the other sides.
Given that angle BAC = 45°, we can use the trigonometric ratio for the side opposite the 45° angle (which is BC) and the hypotenuse (which is AB) to find BC.
Let's assume the length of AB is x.
Using the sine ratio:
sin(45°) = BC / AB
Since sine of 45° is equal to √2 / 2:
√2 / 2 = BC / x
Cross-multiplying:
√2 * x = 2 * BC
Simplifying:
x = 2BC / √2
To simplify further, we can multiply both the numerator and denominator by √2:
x = (2BC / √2) * (√2 / √2)
x = (2BC * 2) / 2
x = 2BC
Therefore, the length of BC is equal to x.
So, BC = x = 10ft (given in the question).
Hence, the length of BC is 10ft.