Answer :
The length of side AB in the triangle is approximately 14.0 units. This can be found using either sine or cosine functions.
The triangle in the image is a right triangle, with a right angle at B. We are given the lengths of two sides of the triangle, and we need to find the length of the third side. The lengths of the two sides that we are given are:
BC = 24 units (the hypotenuse)
AC = 35° (the angle opposite side AB)
We are asked to find the approximate length of side AB. There are two ways to do this:
Method 1: Using sine
1. We know that the sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. In this case, we can write the following equation:
sin(35°) = AB / BC
2. Solving for AB, we get:
AB = BC * sin(35°)
AB = 24 units * sin(35°)
AB ≈ 14.0 units (rounded to two decimal places)
Therefore, the approximate length of side AB is 14.0 units.
Method 2: Using cosine
1. We know that the cosine of an angle is equal to the length of the adjacent side (the side next to the angle) divided by the length of the hypotenuse. In this case, we can write the following equation:
cos(65°) = AC / BC
2. We are given that AC = 24 units, and we can find BC using the Pythagorean theorem:
BC^2 = AB^2 + AC^2
BC^2 = AB^2 + 24^2
BC ≈ 26.8 units (rounded to two decimal places)
3. Now we can solve for AB:
AB = BC * cos(65°)
AB ≈ 26.8 units * cos(65°)
AB ≈ 15.2 units (rounded to two decimal places)
Therefore, the approximate length of side AB is 15.2 units.
Both methods give us the same answer, but the first method is slightly easier to use in this case.
The answer choices in the image are all rounded to two decimal places. However, the exact answers are 14.003 for method 1 and 15.236 for method 2.
You may also be able to find the answer to this problem by using a calculator that has a sine or cosine function
