Math, asked by jaysonongsy, 3 months ago

A rectangle has dimensions 10cm by 5 cm. Determine the measures of the angles at the point where the diagonals intersect.​

Answers

Answered by MANDAR4919
2

Step-by-step explanation:

A rectangle has dimensions 10 cm by 5 cm. Determine the measures of the angles at the point where the diagonals intersect.?

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Answered 1 year ago

A rectangle has dimensions 10cm by 5cm. What are the measures of the two angles at the point where diagonals intersect?

A rectangle has dimensions 10cm by 5cm. What are the measures of the two angles at the point where diagonals intersect?

In your rectangle draw the two diagonals. Can you see this produces 8 triangles, 4 small ones around the point where the diagonals intersect, and 4 right angled triangles each making up half the rectangle. Take one of these large right angled triangles and calculate, using Tangent, the small acute angle in this triangle. It goes like this:

Tan (angle) = opposite side over adjacent side

Tan (angle) = 5/10 = 0.5

Then, using a scientific calculator find the inverse Tan of 0.5. It is approximately 26.565 degrees.

Now use the non right angled triangle that contains the angle you want to work out. Note that the two acute angles in this triangle are equal and the third obtuse angle is your angle. Can you tell me why?

The angles of a triangle in a plane add to 180 degrees so

26.565 + 26.565 + (your angle) = 180 degrees

Solve this equation for (your angle) and you get

(your angle) = 126.87 degrees.

The other angle you want you get by working this out

180 degrees - 126.87 degrees = (your other angle). Can you tell me why this is true?

Done.

Answered by samairaaggarwal4
0

Answer:

In your rectangle draw the two diagonals. Can you see this produces 8 triangles, 4 small ones around the point where the diagonals intersect, and 4 right angled triangles each making up half the rectangle. Take one of these large right angled triangles and calculate, using Tangent, the small acute angle in this triangle. It goes like this:

Tan (angle) = opposite side over adjacent side

Tan (angle) = 5/10 = 0.5

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