Studdy AI Logo
Math  /  Trigonometry

QuestionTan⁡601=x7=\frac{\operatorname{Tan} 60}{1}=\frac{x}{7}=

Studdy Solution

STEP 1

1. The equation involves the tangent of an angle, specifically tan⁡(60∘) \tan(60^\circ) .
2. We need to solve for x x using the given proportion.

STEP 2

1. Calculate the value of tan⁡(60∘)\tan(60^\circ).
2. Set up the proportion and solve for x x .

STEP 3

Calculate the value of tan⁡(60∘)\tan(60^\circ). From trigonometric identities, we know:
tan⁡(60∘)=3\tan(60^\circ) = \sqrt{3}

STEP 4

Set up the proportion using the given equation:
tan⁡(60∘)1=x7\frac{\tan(60^\circ)}{1} = \frac{x}{7}
Substitute the value of tan⁡(60∘)\tan(60^\circ) into the equation:
31=x7\frac{\sqrt{3}}{1} = \frac{x}{7}

STEP 5

Cross-multiply to solve for x x :
3×7=x×1\sqrt{3} \times 7 = x \times 1
Simplify:
x=73x = 7\sqrt{3}
The value of x x is:
73\boxed{7\sqrt{3}}

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