Math / Trigonometry

Question3. 5. 6. 4.

Studdy Solution

STEP 1

What is this asking? We need to find the length of side $x$ in four different right triangles, each with a given angle and side length. Watch out! Make sure your calculator is in degree mode, not radians!
Also, remember SOH CAH TOA!

STEP 2

1. Triangle 3
2. Triangle 4
3. Triangle 5
4. Triangle 6

STEP 3

Alright, in triangle 3, we have an angle of 18 degrees, a side adjacent to it of length 34, and we want to find the opposite side, $x$ .
Which trig function relates opposite and adjacent?
It's tangent!

STEP 4

So, we can write: $\tan(18^\circ) = \frac{x}{34}$

STEP 5

To isolate $x$ , we multiply both sides by 34: $x = 34 \cdot \tan(18^\circ)$

STEP 6

Calculate the result: $x \approx 34 \cdot 0.3249 \approx 11.05$ So, $x$ is approximately 11.05!

STEP 7

For triangle 4, we have an angle of 35 degrees, the opposite side is 9, and we're looking for the adjacent side, $x$ .
Tangent again!

STEP 8

We set up the equation: $\tan(35^\circ) = \frac{9}{x}$

STEP 9

To solve for $x$ , we can multiply both sides by $x$ and then divide by $\tan(35^\circ)$ : $x = \frac{9}{\tan(35^\circ)}$

STEP 10

Calculating that gives us: $x \approx \frac{9}{0.7002} \approx 12.85$ $x$ is approximately 12.85!

STEP 11

Triangle 5 has an angle of 63 degrees, the opposite side is 27, and we want the adjacent side, $x$ .
It's tangent time!

STEP 12

The equation is: $\tan(63^\circ) = \frac{27}{x}$

STEP 13

Solving for $x$ : $x = \frac{27}{\tan(63^\circ)}$

STEP 14

Calculating $x$ : $x \approx \frac{27}{1.9626} \approx 13.76$ $x$ is approximately 13.76!

STEP 15

Finally, triangle 6 has an angle of 30 degrees, opposite side $x$ , and adjacent side 18.
Tangent, tangent, tangent!

STEP 16

Our equation is: $\tan(30^\circ) = \frac{x}{18}$

STEP 17

Isolating $x$ : $x = 18 \cdot \tan(30^\circ)$

STEP 18

Calculating the value of $x$ : $x \approx 18 \cdot 0.5774 \approx 10.39$ So, $x$ is approximately 10.39!

STEP 19

Triangle 3: $x \approx 11.05$ Triangle 4: $x \approx 12.85$ Triangle 5: $x \approx 13.76$ Triangle 6: $x \approx 10.39$

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms