To find out if the triangle is a right triangle, we must check if the following equation is true:
on the left side, we have:
and on the right side, we have:
since on both sides we get 625, we have that the brace forms a right triangle.
Inscribed is a polygon inside a circle with all points on a given point in the circle. Circumscribed is a circle inside a polygon with any given point touching just one point on the polygon. Hope this helped.
Answer:
The answer to your question is 14° and 76°
Step-by-step explanation:
Data
leg 1 = x
leg 2 = x/4
angle 1 = ?
angle 2 = ?
Process
To solve problem use trigonometric functions. We must use the trigonometric function that relates both legs (tangent).
tangent Ф = Opposite side / Adjacent side
-Substitution
tan Ф = (x/4) / x
-Simplification
tan Ф = x / 4x
tan Ф = 1/4
- Find Ф
Ф = tan⁻¹(1/4) = 14°
- Find the other acute angle
The sum of the internal angles in a triangles equals 180°
Ф + Ф₁ + 90° = 180
-Solve for Ф₁
Ф₁ = 180 - 90 - 14
-Result
Ф₁ = 76°
area of triangle = 1/2(3)(4) = 6 in^2
area of rectangle = 3 x 10 = 30 in^2
area of trapezoid = 1/2(3+5)(2) = 8 in^2
area of the figure: 6 in^2 + 30 in^2 + 8 in^2 = 44 in^2
answer
44 in^2
