QuestionSolve the right triangle.
Write your answers as integers or as decimals rounded to the nearest tenth.
Submit
Studdy Solution
STEP 1
What is this asking?
We're given a right triangle with a known side and angle, and we need to find the other two sides and the remaining angle.
Watch out!
Make sure your calculator is in degree mode, not radians!
Also, remember that the angles in a triangle always add up to degrees.
STEP 2
1. Find the missing angle.
2. Find the length of side .
3. Find the length of side .
STEP 3
We know that the sum of angles in any triangle is degrees.
We're given that is degrees and is degrees (because it's a right triangle!). So, to find , we can subtract the known angles from :
STEP 4
Therefore, is ** degrees**.
STEP 5
We can use the **tangent function** because we know the angle ( degrees) and the hypotenuse (), and we want to find the opposite side ().
Remember, tangent is opposite over adjacent:
But we don't know yet!
So, let's use sine instead.
Sine is opposite over hypotenuse, and we know both the angle and the hypotenuse :
STEP 6
**Substitute** the known values:
STEP 7
**Multiply** both sides by to isolate :
STEP 8
**Calculate** the value: Rounding to the nearest tenth gives us \ ****.
STEP 9
Now we can use the **cosine function** since we know the angle ( degrees) and the hypotenuse (), and we want to find the adjacent side ().
Cosine is adjacent over hypotenuse:
STEP 10
**Substitute** the known values:
STEP 11
**Multiply** both sides by to isolate :
STEP 12
**Calculate** the value: Rounding to the nearest tenth gives us ****.
STEP 13
degrees
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