Which represents an exterior angle of triangle ABF? ∠BAD ∠AFE ∠CAD ∠CAB
1 answer:
The angle that represents an exterior angle of the given triangle is: D. ∠CAB.
<h3>What is an Exterior Angle of a Triangle?</h3>An exterior angle of a triangle is the angle that is located outside a triangle on an extended adjacent side of the triangle.
In the image given, and considering the options we have, ∠CAB is located outside a triangle ABF on an extended adjacent side CF of the triangle.
Therefore, the answer is: D. ∠CAB.
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Answer:
a) 1650 m
b) 1677.05 m
Step-by-step explanation:
Hi there!
<u>1) Determine what is required for the answers</u>
For part A, we're asked for solve for the horizontal distance in which the road will rise 300 m. In other words, we're solving for the distance from point A to point C, point C being the third vertex of the triangle.
For part B, we're asked to solve for the length of the road, or the length of AB.
<u>2) Prove similarity</u>
In the diagram, we can see that there are two similar triangles: Triangle AXY and ABC (please refer to the image attached).
How do we know they're similar?
- Angles AYX and ACB are corresponding and they both measure 90 degrees
- Both triangles share angle A
Therefore, the two triangles are similar because of AA~ (angle-angle similarity).
<u>3) Solve for part A</u>
Recall that we need to find the length of AC.
First, set up a proportion. XY corresponds to BC and AY corresponds to AC:
Plug in known values
Cross-multiply
Therefore, the road will rise 300 m over a horizontal distance of 1650 m.
<u>4) Solve for part B</u>
To find the length of AB, we can use the Pythagorean theorem:
where c is the hypotenuse of a right triangle and a and b are the other sides
Plug in 300 and 1650 as the legs (we are solving for the longest side)
Therefore, the length of the road is approximately 1677.05 m.
I hope this helps!
