Forty-five and Thirty
Pro Problems > Math > Geometry > TrianglesForty-five and Thirty
Two of the angles of a triangle are 45 degrees and 30 degrees. The altitude from the third angle has length 15 units. What is the triangle's area?
Solution
In order to make it feasible for teachers to use these problems in their classwork, no solutions are publicly visible, so students cannot simply look up the answers. If you would like to view the solutions to these problems, you must have a Virtual Classroom subscription.
Similar Problems
Angle Riddle
The angles of a triangle meet the following criteria:
- All the angle measures are prime numbers.
- All the angle measures are distinct.
- Exactly two of my angle measures are palindromic.
- The difference between my two largest angle measures is a two digit number x.
- One of the digits of x is twice the other digit.
Arithmetic Angles
The angles of a triangle are in arithmetic progression, and the difference between the largest and smallest angle is 42 degrees. What are the three angles?
Angle Measure
Line segment AB is intersected by segment DC, with D on AB, between A and B.
In triangle ADC, m∠ADC = 30º + x and m∠DAC = 50º
In triangle ABC, m∠ACB = 115º + x
In triangle CDB, m∠CDB = 140º + x
Find m∠CBD.
Two Triangles with Angle Measures
In a triangle, the angles measures are: 3x + 44, x, and 2x - 20. In a second triangle, two of the angle measures are x + 20 and 2x - 5. What is the measure of the third angle?
Triangle in a Square
If the perimeter of the triangle (in linear units) is equal to the area of the triangle (in square units), what is the length of the side of the square?
Triangle in a Square
Triangle ABC is inside square ABDE, and C lies along side DE. If the area of the triangle is 24 square units, what is the length of AB?
Triangle and Rectangle
In the diagram displayed, the triangle splits the rectangle into three similar triangles. Find the value of AD2 divided by the product of DE and EC.
Angle Bisector
In the diagram shown,
m ∠DCF = 80
m ∠ACF = 30
m ∠FBD = 50.
If segment BF bisects ∠ABD, find m ∠BAC.
Split Triangle
Segment AD is drawn in triangle ABC, with D on side BC. Given the following information, determine the measure of angle ADB.
measure of angle BAD = x
measure of angle CAD = 2x
measure of angle ADC = 2y
measure of angle ABD = y
measure of angle ACD = x + y
Quadratic Triangle
The angles in a triangle have measures x2 - 5, 2x + 18, and x + 37. What is the measure of the largest angle in the triangle?
Blogs on This Site
Like us on Facebook to get updates about new resources