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:

$a=c=\dfrac{ 2 }{ 3 } b \ \\ \cos B=\dfrac{ b/2 }{ a } \ \\ \cos B=\dfrac{ b/2 }{ \dfrac{ 2 }{ 3 } b } \ \\ \cos B=\dfrac{ 1/2 }{ \dfrac{ 2 }{ 3 } } \ \\ \ \\ B_{1}=\arccos(\dfrac{ 1/2 }{ 2/3 } ) \doteq 0.7227 \ \text{rad} \ \\ \ \\ B=B_{1} \rightarrow \ ^\circ =B_{1} \cdot \ \dfrac{ 180 }{ \pi } \ \ ^\circ =0.722734247813 \cdot \ \dfrac{ 180 }{ \pi } \ \ ^\circ =41.40962 \ \ ^\circ =41.41 ^\circ =41^\circ 24'35"$

Try calculation via our triangle calculator.

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

Tips to related online calculators

Next similar math problems:

1. 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'.
2. 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.
3. 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.
4. 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?
5. One side
One side is 36 long with a 15° incline. What is the height at the end of that side?
6. 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?
7. Power line pole
From point A, the power line pole is seen at an angle of 18 degrees. From point B to which we get when going from point A 30m away from the column at an angle of 10 degrees. Find the height of the power pole.
8. 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?
9. The rescue helicopter
The rescue helicopter is above the landing site at a height of 180m. The site of the rescue operation can be seen from here at a depth angle of 52° 40 '. How far will the helicopter land from the rescue site?
10. 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?
11. Cosine
The point (8, 6) is on the terminal side of angle θ. cos θ = ?
12. Cosine
Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 3 and 8 and with the hypotenuse 8.544.
13. 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?
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: