Right triangle

It is given a right triangle
angle alpha of 90 degrees
beta angle of 55 degrees
c = 10 cm
use Pythagorean theorem to calculate sides a and b

Correct answer:

a =  17.4345 cm
b =  14.2815 cm

Step-by-step explanation:

$$\begin{gathered} c=10\text{ cm } \\ \beta =55\text{ ° } \\ {a}^2=b^2+c^2 \\ \cos \beta =c\mathrm{/}a \\ a=c\mathrm{/}\cos \beta \mathrm{°}=c\mathrm{/}\cos 55\mathrm{°}=10\mathrm{/}\cos 55\mathrm{°}=10\mathrm{/}0.573576=17.434=17.4345\text{ cm} \end{gathered}$$

$b=\sqrt{a^2-c^2}=\sqrt{17.4345^2-10^2}=14.2815\text{ cm}$

Try calculation via our triangle calculator.

Try another example

Related math problems and questions:

• 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)
• 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'.
• Centre of the hypotenuse
  For the interior angles of the triangle ABC, alpha beta and gamma are in a ratio of 1: 2: 3. The longest side of the AB triangle is 30 cm long. Calculate the perimeter of the triangle CBS if S is the center of the side AB.
• Right triangle
  A right triangle ABC is given, c is a hypotenuse. Find the length of the sides a, b, the angle beta if c = 5 and angle alfa = A = 35 degrees.
• Rectangular
  Rectangular triangle KLM with right angle at vertex L, angle beta at vertex K and angle alpha at vertex M. Angle at vertex M = 65°, side l = 17.5 cm. Use Pythagorean theorems and trigonometric functions to calculate the lengths of all sides and the angle
• Triangle SAS
  Calculate the triangle area and perimeter, if the two sides are 51 cm and 110 cm long and angle them clamped is 130 °.
• Right angled triangle 3
  Side b = 1.5, hypotenuse angle A = 70 degrees, Angle B = 20 degrees. Find its unknown sides length.
• Right angle
  In a right triangle ABC with a right angle at the apex C, we know the side length AB = 24 cm and the angle at the vertex B = 71°. Calculate the length of the legs of the triangle.
• Tower's view
  From the church tower's view at the height of 65 m, the top of the house can be seen at a depth angle of alpha = 45° and its bottom at a depth angle of beta = 58°. Calculate the height of the house and its distance from the church.
• The bases
  The bases of the isosceles trapezoid ABCD have lengths of 10 cm and 6 cm. Its arms form an angle α = 50˚ with a longer base. Calculate the circumference and content of the ABCD trapezoid.
• Medians in right triangle
  It is given a right triangle, angle C is 90 degrees. I know it medians t1 = 8 cm and median t2 = 12 cm. .. How to calculate the length of the sides?
• Rectangle
  Calculate the length of the side GN and diagonal QN of rectangle QGNH when given: |HN| = 25 cm and angle ∠ QGH = 28 degrees.
• Right triangle
  Calculate the missing side b and interior angles, perimeter, and area of ​​a right triangle if a=10 cm and hypotenuse c = 16 cm.
• Two forces
  The two forces F1 = 580N and F2 = 630N, have an angle of 59 degrees. Calculate their resultant force, F.
• Calculate
  Calculate the area of triangle ABC, if given by alpha = 49°, beta = 31°, and the height on the c side is 9cm.
• Ratio in trapezium
  The height v and the base a, c in the trapezoid ABCD are in the ratio 1: 6: 3, its content S = 324 square cm. Peak angle B = 35 degrees. Determine the perimeter of the trapezoid
• Space diagonal angles
  Calculate the angle between the body diagonal and the side edge c of the block with dimensions: a = 28cm, b = 45cm and c = 73cm. Then, find the angle between the body diagonal and the plane of the base ABCD.