Triangle and its heights

Calculate the length of the sides of the triangle ABC, if va=5 cm, vb=7 cm and side b is 5 cm shorter than side a.

Result

a =  17.5 cm
b =  12.5 cm
c =  7.84 cm

Solution:   Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...): Be the first to comment! To solve this verbal math problem are needed these knowledge from mathematics:

Pythagorean theorem is the base for the right triangle calculator. Cosine rule uses trigonometric SAS triangle calculator. See also our trigonometric triangle calculator.

Next similar examples:

1. Euclid 5 Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm.
2. Triangle IRT In isosceles right triangle ABC with right angle at vertex C is coordinates: A (-1, 2); C (-5, -2) Calculate the length of segment AB.
3. Right triangle trigonometrics Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60° and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent)
4. Triangle Calculate the area of ​​the triangle ABC if b = c = 17 cm, R = 19 cm (R is the circumradius).
5. Angles by cosine law Calculate the size of the angles of the triangle ABC, if it is given by: a = 3 cm; b = 5 cm; c = 7 cm (use the sine and cosine theorem).
6. Isosceles IV In an isosceles triangle ABC is |AC| = |BC| = 13 and |AB| = 10. Calculate the radius of the inscribed (r) and described (R) circle.
7. Sines In ▵ ABC, if sin(α)=0.5 and sin(β)=0.6 calculate sin(γ)
8. Triangle ABC In a triangle ABC with the side BC of length 2 cm The middle point of AB. Points L and M split AC side into three equal lines. KLM is isosceles triangle with a right angle at the point K. Determine the lengths of the sides AB, AC triangle ABC.
9. Spruce height How tall was spruce that was cut at an altitude of 8m above the ground and the top landed at a distance of 15m from the heel of the tree?
10. Right 24 Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 unequal segments. The length of one segment is 5 cm. What is the area of the triangle? Thank you.
11. Cable car Cable car rises at an angle 45° and connects the upper and lower station with an altitude difference of 744 m. How long is "endless" tow rope?
12. One side One side is 36 long with a 15° incline. What is the height at the end of that side?
13. Laws From which law follows directly the validity of Pythagoras' theorem in the right triangle? ? The double ladder is 8.5m long. It is built so that its lower ends are 3.5 meters apart. How high does the upper end of the ladder reach? 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? Is true equality? ?