Question

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

Answer 1

Two opposite rhombus's angles have the measure of approximately 30° and two another angles have the measure of approximately 150°.

Explanation:

Find the area of the rhombus in two different ways.

1. Use formula

`A=ah,`

where a is a side length and h is a height of the rhombus.

Hence,

`A=241\cdot 120\ m^2`

2. Use formula

`A=a^2\sin \alpha,`

where
`\alpha` is one of rhombus's angles.

So,

`A=241^2\sin \alpha\ m^2`

3. Equate both expressions:

`241\cdot 120=241^2\sin \alpha\\ \\\sin \alpha =(120)/(241)\\ \\\alpha \approx 30^(\circ)`

Therefore, two opposite rhombus's angles have the measure of approximately 30° and two another angles have the measure of approximately 150°.

Answer 2

29.863°, 29.863°, 150.137°, 150.137°

Explanation:

The explanation above was perfectly correct and reasonable, the only issue was that the person who did it rounded the numbers instead of giving you guys the full decimal, which means the grading systems you guys probably imputed your answers into marked it wrong, and thus you gave this person one star. Do the problem yourself by plugging the numbers into the formula in the explanation above.

P.S. don't forget the degree (°) symbol