Given that △ABC is a right triangle with ∠A=90° , ∠B=25° , and BC=5 inches , which of the following correctly uses the sine ratio to find the length of AC¯¯¯¯¯¯¯¯ ?(1 point)
Responses
AC=5/sin65°
AC=5 sin25°
AC=5 sin65°
AC=5/sin25°
The correct answer is:
AC = 5/sin25°
The original height of the Great Pyramid of Giza was 481 feet. The side of the pyramid rose at an angle of approximately 52° . Which of the following correctly uses the sine ratio to find the length from the bottom to the top of the pyramid to the nearest foot?(1 point)
Responses
610 feet
610 feet
781 feet
781 feet
296 feet
296 feet
379 feet
The correct answer is:
781 feet
A 16-foot ladder leans against a wall so that the ladder’s angle of elevation is 55°. Find x, the distance between the foot of the ladder and the base of the building. Use cosine to solve for the missing side and round your answer to the nearest hundredth.(1 point)
Responses
x=9.18 ft.
x equals 9.18 ft.
x=52.87 ft.
x equals 52.87 ft.
x=27.90 ft.
x equals 27.90 ft.
x=13.11 ft.
The correct answer is:
x = 9.18 ft.
Given the expression sin(3x+10°)=cos(2x−10°) , which of the following uses the relationship between the sine and cosine of complementary angles to correctly determine the value of x?(1 point)
Responses
18°
18°
22°
22°
36°
36°
16°
The correct answer is:
16°
A right triangle has two acute angles, θ and ϕ , so that cosϕ=x+0.2 and sinθ=2x−0.5 . What is the value of x?(1 point)
Responses
10
10
0.7
0.7
1
1
0.07
To find the value of x, we can solve the given equations simultaneously.
From cosϕ = x + 0.2, we have:
ϕ = arccos(x + 0.2)
From sinθ = 2x - 0.5, we have:
θ = arcsin(2x - 0.5)
Since θ and ϕ are acute angles of a right triangle, we know that they are complementary angles, which means that their sum is equal to 90°.
Therefore, we can write the equation:
θ + ϕ = 90°
Substituting the expressions for θ and ϕ, we have:
arcsin(2x - 0.5) + arccos(x + 0.2) = 90°
To find the value of x, we would need additional information or a numerical equation to solve. None of the given options can determine the exact value of x based on the given information.