Math  /  Trigonometry

QuestionQuestion Express sinC\sin C as a fraction in simplest terms.
Answer Attempt 2 out of 2 sinC=\sin C= \square Submit Answer \sqrt{ } MacBook Air

Studdy Solution

STEP 1

1. The triangle CDE \triangle CDE is a right triangle with a right angle at D D .
2. The side lengths are given as CD=86 CD = \sqrt{86} and DE=35 DE = \sqrt{35} .
3. The hypotenuse CE CE can be found using the Pythagorean theorem.
4. The sine of an angle in a right triangle is the ratio of the length of the opposite side to the hypotenuse.

STEP 2

1. Calculate the length of the hypotenuse CE CE using the Pythagorean theorem.
2. Find sinC \sin C using the definition of sine in a right triangle.

STEP 3

Use the Pythagorean theorem to calculate the hypotenuse CE CE .
CE=CD2+DE2 CE = \sqrt{CD^2 + DE^2}
Substitute the given values:
CE=(86)2+(35)2 CE = \sqrt{(\sqrt{86})^2 + (\sqrt{35})^2}

STEP 4

Simplify the expression for CE CE .
CE=86+35 CE = \sqrt{86 + 35}

STEP 5

Add the values under the square root.
CE=121 CE = \sqrt{121}

STEP 6

Take the square root of 121 to find the hypotenuse.
CE=11 CE = 11

STEP 7

Use the definition of sine to find sinC \sin C .
sinC=oppositehypotenuse \sin C = \frac{\text{opposite}}{\text{hypotenuse}}

STEP 8

Identify the opposite side to angle C C and the hypotenuse.
The opposite side to C \angle C is DE DE , which is 35 \sqrt{35} , and the hypotenuse is CE CE , which is 11 11 .
sinC=3511 \sin C = \frac{\sqrt{35}}{11}
Solution: sinC=3511 \sin C = \frac{\sqrt{35}}{11}

Was this helpful?

Studdy solves anything!

banner

Start learning now

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

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord