# Isosceles triangle 10

In an isosceles triangle, the equal sides are 2/3 of the length of the base. Determine the measure of the base angles.

Result

B =  41.41 °

#### Solution:

$a = c = \dfrac{ 2 }{ 3 } b \ \\ \cos B = \dfrac{ b/2 }{ a } \ \\ \cos B = \dfrac{ b/2 }{ \dfrac{ 2 }{ 3 } b } \ \\ \cos B = \dfrac{ 1/2 }{ \dfrac{ 2 }{ 3 } } \ \\ \ \\ B_{ 1 } = \arccos(\dfrac{ 1/2 }{ 2/3 } ) \doteq 0.7227 \ rad \ \\ \ \\ B = B_{ 1 } \rightarrow \ ^\circ = B_{ 1 } \cdot \ \dfrac{ 180 }{ \pi } \ \ ^\circ = 41.4096221092 \ \ ^\circ = 41.41 ^\circ = 41^\circ 24'35"$

Try calculation via our triangle calculator.

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...): Be the first to comment! ## Next similar math problems:

1. Flowerbed Flowerbed has the shape of an isosceles obtuse triangle. Arm has a size 5.5 meters and an angle opposite to the base size is 94°. What is the distance from the base to opposite vertex?
2. Right triangle Calculate the length of the remaining two sides and the angles in the rectangular triangle ABC if a = 10 cm, angle alpha = 18°40'.
3. The Eiffel Tower The top of the Eiffel Tower is seen from a distance of 600 meters at an angle of 30 degrees. Find the tower height.
4. Reflector Circular reflector throws light cone with a vertex angle 49° and is on 33 m height tower. The axis of the light beam has with the axis of the tower angle 30°. What is the maximum length of the illuminated horizontal plane?
5. Maple Maple peak is visible from a distance 3 m from the trunk from a height of 1.8 m at angle 62°. Determine the height of the maple.
6. Building The building I focused at an angle 30°. When I moved 5 m building I focused at an angle 45°. What is the height of the building?
7. One side One side is 36 long with a 15° incline. What is the height at the end of that side?
8. Steeple Steeple seen from the road at an angle of 75°. When we zoom out to 25 meters, it is seen at an angle of 20°. What is high?
9. Tree Between points A and B is 50m. From A we see a tree at an angle 18°. From point B we see the tree in three times bigger angle. How tall is a tree?
10. High wall I have a wall 2m high. I need a 15 degree angle (upward) to second wall 4 meters away. How high must the second wall?
11. Triangle Calculate the area of ​​the triangle ABC if b = c = 17 cm, R = 19 cm (R is the circumradius).
12. Tree How tall is the tree that observed in the visual angle of 52°? If I stand 5 m from the tree and eyes are two meters above the ground.
13. Cable car 2 Cable car rises at an angle 41° and connects the upper and lower station with an altitude difference of 1175 m. How long is the track of cable car?
14. Trigonometry Is true equality? ?
15. Holidays - on pool Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?
16. Theorem prove We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
17. Reference angle Find the reference angle of each angle: