A rectangle has dimensions 10cm by 5 cm. Determine the measures of the angles at the point where the diagonals intersect.
Answers
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.?
How do I motivate myself to study?
Sometimes the act of studying may seem tiresome. It’s normal — so don’t beat yourself up for it. Instead, learn how to conquer it
Frank Gross
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.
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