Ashadow cast by a building is 50 ft long when the angle of inclination of the sun is 30 degrees. how tall is the building?

28.87 ft

Step-by-step explanation:

Triangles And Trigonometry

In right triangles, some special relationships hold like Pythagoras's theorem and the three basic definitions of trigonometric functions. If a,b,c are the length of the sides of a right triangle, being c its hypotenuse and a and b its legs, then

where b is the side opposite to the angle and a is the side adjacent to the angle

Please refer to the image below

In our problem, the building is the height of the triangle (b), its shadow is the width (a), and the distance from the tip of the shadow and the top of the building is the hypotenuse (c). We know the angle of inclination is 30°. The known side is one leg of the triangle, and the height of the building is the other leg. The relation to use is

Solving for b

answer:   the paragraph proof is mentioned below.

step-by-step explanation:

given: in a δxwy where

such that, ∠wzx ≅ ∠yzx and zw≅zy

we have to prove that: segment zx is a perpendicular bisector of segment wy.

prove: since, zw≅zy ⇒ ∠wzy is a supplementary angle.

then, ∠wzy= 180°

⇒∠wzx + ∠yzx = 180° ( because xz divides ∠wzy into two parts)

but, ∠wzx ≅ ∠yzx ( given)

⇒∠wzy+∠wzy=180° ( by substitution)

⇒2∠wzy=180°

⇒∠wzy=90°

⇒∠wzy=∠yzx =90°

therefore, xz⊥wy where wz=zy

⇒zx is a perpendicular bisector of wy.