The roof of a solar house is elevated by an angle of 50° at the front and by an angle of 40° at the back. Write an equation to determine the angle at the peak. Use <P. solve the equation
draw triangle
40 + 50 + p = 180
p = 180 - 90
p = 90
Am not really understanding this question. Can u pls explain it more properly???????
To determine the angle at the peak of the solar house, we can consider the triangle formed by the front elevation, the back elevation, and the roof peak. Let's label the angle at the peak as <P.
Based on the given information, we have:
Front elevation angle: 50°
Back elevation angle: 40°
In a triangle, the sum of interior angles is always 180°. Therefore, we can set up the equation:
Front elevation angle + Back elevation angle + Angle at the peak = 180°
Substituting the given values:
50° + 40° + <P = 180°
Simplifying the equation:
90° + <P = 180°
To solve for <P, we can isolate it by subtracting 90° from both sides:
<P = 180° - 90°
<P = 90°
Therefore, the angle at the peak is 90°.
To determine the angle at the peak, we can use the fact that the sum of the angles of a triangle is always 180 degrees.
Let's denote the angle at the peak as 'P'. We know that the angle at the front is 50 degrees, and the angle at the back is 40 degrees.
Therefore, the equation to determine the angle at the peak can be written as:
P + 50 + 40 = 180
This equation states that the sum of the angle at the peak, the angle at the front, and the angle at the back is equal to 180 degrees (the sum of the angles in a triangle).
Now, let's solve the equation to find the value of angle 'P':
P + 90 = 180 (combining like terms)
P = 180 - 90 (subtracting 90 from both sides)
P = 90
Therefore, the angle at the peak is 90 degrees.