1. In ABC, A is a right angle, and m B=45*.
Side CA also has a length of 17ft just to let everyone know.
What is the length of BC? If the answer is not an integer, leave it in simplest radical form. The diagram is not shown to scale.
A) 54 ft
B) 17 sqrt 3 ft.
C) 17 sqrt 2 ft.
D) 17 ft
I'm really confused on how to get this.
I saw someone do Sin 45 17/bc, they did it with different numbers so I plugged 17 in instead.
Where do I go from there?
I'm pretty sure it's
17 sqrt 2 ft.
not 100% sure though
Well, let's start by addressing your confusion. It seems like you're on the right track! The sin of an angle is equal to the length of the opposite side divided by the length of the hypotenuse. In this case, the angle is 45 degrees, the opposite side is BC, and the hypotenuse is 17 ft.
So, we have sin 45° = BC/17. To solve for BC, we can rearrange the equation to BC = 17 * sin 45°.
Now, let's evaluate sin 45°. Sin 45° is equal to the square root of 2 divided by 2. So, BC = 17 * (sqrt(2)/2).
Simplifying, we get BC = 17sqrt(2)/2. Since we want the answer in simplest radical form, this corresponds to answer choice C) 17 sqrt 2 ft.
I hope that clears things up!
To find the length of BC, we can use the sine ratio in a right triangle. The sine ratio states that the sine of an angle is equal to the ratio of the length of the opposite side to the length of the hypotenuse.
In this case, angle B is 45 degrees and BC is the opposite side, while CA is the hypotenuse. Let's set up the equation using the sine ratio:
sin(45°) = BC/17
To solve for BC, we need to isolate it on one side of the equation. Since the sine of 45 degrees is equal to 1/sqrt(2) (or approximately 0.707), we can substitute that in:
1/sqrt(2) = BC/17
To get BC alone, we can multiply both sides of the equation by 17:
(17/sqrt(2)) = BC
Simplifying the radical in the denominator:
(17 sqrt(2)/sqrt(2) * sqrt(2)/sqrt(2)) = BC
(17 sqrt(2) * sqrt(2))/(2) = BC
(17 * 2)/(2) = BC
34/2 = BC
BC = 17
Therefore, the length of BC is 17ft.
So, the answer is D) 17 ft.
To determine the length of side BC in triangle ABC, you can use the trigonometric ratio of sine. By using the sine function, you can relate the angle B and the lengths of sides BC and AC.
The sine function is defined as sin(angle) = opposite/hypotenuse. In this case, angle B is 45 degrees and the opposite side is BC. The hypotenuse is side AC, which is given as 17 ft.
To solve for BC, you can rearrange the sine function: BC = AC * sin(angle B).
Plugging in the values, BC = 17 ft * sin(45 degrees).
Now, you need to evaluate the value of sin(45 degrees). Since sin(45 degrees) is a common value in trigonometry, you can find it exactly. The exact value of sin(45 degrees) is 1/sqrt(2).
Substituting this value into the equation, BC = 17 ft * (1/sqrt(2)). To simplify this, you multiply the numerator and denominator by sqrt(2): BC = 17 ft * (1/sqrt(2)) * (sqrt(2)/sqrt(2)).
Simplifying further, BC = 17 ft * sqrt(2)/2.
Therefore, the length of side BC is 17 ft * sqrt(2)/2, which is option C) 17 sqrt(2) ft.
quite simple really.
since angle A = 90° and angle B = 45°, then the other angle is also 45°, and the triangle is isosceles, thus the other two sides are equal.
let each side be x
x^2 + x^2 = 17^2
2x^2 = 289
x^2 = 289/2
x = 17/√2
= 17/√2 * √2/√2 = 17√2/2
all your answers choices are incorrect.
check:
(17√2/2)^2 + (17√2/2)^2
= 289/2 + 289/2 = 289