What are the values of w and x in the triangle below? Round answer to tenth. The triangle is scalene and the smaller one in the larger one has 38 degrees in its bottom right corner. The big triangle is 19 degrees in its bottom right corner. The height is 14. The answers are as below.
w=10.9, x=15.8
w=10.9, x=4.8
w=17,9, x=40.7
w=17.9, x=22.8
I’m really stuck on this so any help/explanation would be great.
To solve this problem, we can use the trigonometric ratios, specifically the tangent function.
First, let's label the sides of the smaller triangle as follows:
- The side opposite the 38-degree angle is "x"
- The side adjacent to the 38-degree angle is "w"
Now, let's apply the tangent function to the smaller triangle:
tan(38 degrees) = x / w
Rearranging the equation, we have:
x = w * tan(38 degrees)
Now, let's move on to the larger triangle. We'll label the sides as follows:
- The side opposite the 19-degree angle is "x"
- The side adjacent to the 19-degree angle is "w" (same as in the smaller triangle)
- The height of the triangle is given as 14.
Using the tangent function once again, we can write an equation with the larger triangle:
tan(19 degrees) = 14 / x
Rearranging the equation, we have:
x = 14 / tan(19 degrees)
By substituting the expression for "x" derived from the smaller triangle into the equation for "x" in the larger triangle, we can solve for "w":
14 / tan(19 degrees) = w * tan(38 degrees)
Let's calculate these values:
1. Convert 38 and 19 degrees to radians:
38 degrees = 0.6632251 radians
19 degrees = 0.3316126 radians
2. Calculate the value of "w":
w = (14 / tan(19 degrees)) / tan(38 degrees)
w ≈ 10.9 (rounded to the nearest tenth)
3. Substitute the value of "w" into the equation for "x" in the smaller triangle:
x = w * tan(38 degrees)
x ≈ 15.8 (rounded to the nearest tenth)
Therefore, the correct answer is:
w = 10.9, x = 15.8