Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

An awning that covers a sliding glass door that is 8888 inches tall forms an angle of 5050 degrees with the wall. The purpose of the awning is to prevent sunlight from entering the house when the angle of elevation of the sun is more than X=55X = 55 degrees. See the figure. Find the length LL of the awning.

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Grade 8right chevron icon
Interpreting Linear Expressionsright chevron icon

Full solution

Q. An awning that covers a sliding glass door that is 8888 inches tall forms an angle of 5050 degrees with the wall. The purpose of the awning is to prevent sunlight from entering the house when the angle of elevation of the sun is more than X=55X = 55 degrees. See the figure. Find the length LL of the awning.
  1. Identify Triangle: Identify the triangle formed by the awning, wall, and ground. The awning forms the hypotenuse, and the height of the door (8888 inches) is the opposite side of the 5050-degree angle.
  2. Use Sine Function: Use the sine function to find the length of the awning (hypotenuse). The sine of an angle in a right triangle is the opposite side divided by the hypotenuse. So, sin⁡(50∘)=88L\sin(50^\circ) = \frac{88}{L}.
  3. Rearrange Equation: Rearrange the equation to solve for LL: L=88sin⁡(50°)L = \frac{88}{\sin(50°)}. Calculate sin⁡(50°)\sin(50°) using a calculator.
  4. Perform Calculation: Perform the calculation: sin⁡(50∘)≈0.7660\sin(50^\circ) \approx 0.7660. So, L=880.7660≈114.88L = \frac{88}{0.7660} \approx 114.88 inches.

More problems from Interpreting Linear Expressions

Question
Simplify the expression:\newline7z2+3z27z^2 + 3z^2 \newline ______
Get tutor helpright-arrow

Posted 7 months ago

Question
Simplify the expression:\newline10f+8f−9f−6f10f + 8f - 9f - 6f\newline____
Get tutor helpright-arrow

Posted 7 months ago

Question
Subtract.\newline(3h+6)−(3h+2)(3h + 6) - (3h + 2)\newline____
Get tutor helpright-arrow

Posted 7 months ago

Question
Simplify the expression:\newline2p−p2p - p \newline______
Get tutor helpright-arrow

Posted 8 months ago

Question
A school charges $6\$6 per ticket to a dance. They spend $300\$300 on music and decorations. The expression 6n−3006n-300 describes the amount of profit the school makes from the dance if nn students buy tickets. What does 6n6n represent in this context?\newlineChoices:\newline(A)The amount of money the school charges for all `\n` tickets\newline(B)The amount of money the school spends on the dance\newline(C)The number of students who buy tickets\newline(D)The profit the school earns per ticket
Get tutor helpright-arrow

Posted 8 months ago

Question
Which is equal to cos⁡60∘ \cos 60^\circ ? \newlineChoices:\newline(A) sin⁡30∘ \sin 30^\circ \newline(B) sin⁡60∘ \sin 60^\circ \newline(C) cos⁡30∘ \cos 30^\circ \newline(D) cos⁡60∘ \cos 60^\circ
Get tutor helpright-arrow

Posted 9 months ago

Question
Which is equal to sin⁡45∘\sin 45^\circ? \newlineChoices:\newline(A) cos⁡45∘\cos 45^\circ\newline(B) cos⁡55∘\cos 55^\circ\newline(C) sin⁡55∘\sin 55^\circ\newline(D) sin⁡35∘\sin 35^\circ
Get tutor helpright-arrow

Posted 7 months ago

Question
Which is equal to cos⁡75∘\cos 75^\circ? \newlineChoices:\newline(A) sin⁡15∘\sin 15^\circ\newline(B) sin⁡75∘\sin 75^\circ\newline(C) cos⁡15∘\cos 15^\circ\newline(D) cos⁡25∘\cos 25^\circ
Get tutor helpright-arrow

Posted 7 months ago

Question
Which is equal to sin⁡30∘ \sin 30^\circ ? \newlineChoices:\newline(A) cos⁡60∘ \cos 60^\circ \newline(B) cos⁡30∘ \cos 30^\circ \newline(C) sin⁡60∘ \sin 60^\circ \newline(D) sin⁡30∘ \sin 30^\circ
Get tutor helpright-arrow

Posted 7 months ago

Question
Which is equal to cos⁡45∘ \cos 45^\circ ? \newlineChoices:\newline(A) sin⁡45∘ \sin 45^\circ \newline(B) sin⁡55∘ \sin 55^\circ \newline(C) cos⁡55∘ \cos 55^\circ \newline(D) cos⁡35∘ \cos 35^\circ
Get tutor helpright-arrow

Posted 7 months ago

View all (79)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant