MATH SOLVE

3 months ago

Q:
# 33 The length of a side of a rhombus is 241m. The length of its height is 120m. Find the measures of its angles.

Accepted Solution

A:

Answer:Two opposite rhombus's angles have the measure of approximately 30° and two another angles have the measure of approximately 150°.Step-by-step explanation:Find the area of the rhombus in two different ways.1. Use formula[tex]A=ah,[/tex]where a is a side length and h is a height of the rhombus.Hence,[tex]A=241\cdot 120\ m^2[/tex]2. Use formula[tex]A=a^2\sin \alpha,[/tex]where [tex]\alpha[/tex] is one of rhombus's angles.So,[tex]A=241^2\sin \alpha\ m^2[/tex]3. Equate both expressions:[tex]241\cdot 120=241^2\sin \alpha\\ \\\sin \alpha =\dfrac{120}{241}\\ \\\alpha \approx 30^{\circ}[/tex]Therefore, two opposite rhombus's angles have the measure of approximately 30° and two another angles have the measure of approximately 150°.