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.

Correct result:

b =  12.49 cm
A =  38.6822 °
B =  51.3178 °
C =  90 °
o =  38.49 cm
S =  62.45 cm²

Solution:

$$\begin{gathered} a=10\text{ cm } \\ c=16\text{ cm } \\ b=\sqrt{c^2-a^2}=\sqrt{16^2-10^2}=2\sqrt{39}=12.49\text{ cm} \end{gathered}$$

$A=180\mathrm{/}\pi \cdot (\arcsin (a\mathrm{/}c))=180\mathrm{/}3.1416\cdot (\arcsin (10\mathrm{/}16))=38.6822^{\circ }=38^{\circ }40^{\mathrm{\prime }}56\mathrm{"}$

$B=90-A=90-38.6822=51.3178^{\circ }=51^{\circ }19^{\mathrm{\prime }}4\mathrm{"}$

$C=90=90^{\circ }$

$o=a+b+c=10+12.49+16=38.49\text{ cm}$

$S=a\cdot b\mathrm{/}2=10\cdot 12.49\mathrm{/}2=10\sqrt{39}=62.45{\text{cm}}^2$

Try calculation via our triangle calculator.

Try another example

Showing 0 comments:

Related math problems and questions:

• IS triangle
  Calculate interior angles of the isosceles triangle with base 40 cm and legs 22 cm long.
• Triangle in a square
  In a square ABCD with side a = 6 cm, point E is the center of side AB and point F is the center of side BC. Calculate the size of all angles of the triangle DEF and the lengths of its sides.
• 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
  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
• Right triangle eq2
  Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
• Angles
  Determine the interior angles of a rhombus with area 319.1 cm² and perimeter 72 cm.
• 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.
• 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 °.
• Hypotenuse
  Calculate the length of the hypotenuse of a right triangle if the length of one leg is 4 cm and its content area is 16 square centimeters.
• Pentagon
  Calculate the length of side, circumference and area of a regular pentagon, which is inscribed in a circle with radius r = 6 cm.
• The aspect ratio
  The aspect ratio of the rectangular triangle is 13: 12: 5. Calculate the internal angles of the triangle.
• 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.
• The right triangle
  In the right triangle ABC with right angle at C we know the side lengths AC = 9 cm and BC = 7 cm. Calculate the length of the remaining side of the triangle and the size of all angles.
• Triangle ABC v2
  Area of the triangle is 12 cm square. Angle ACB = 30º , AC = (x + 2) cm, BC = x cm. Calculate the value of x.
• Median
  In triangle ABC is given side a=10 cm and median ta= 13 cm and angle gamma 90°. Calculate length of the median tb.
• Isosceles trapezoid
  Find the area of an isosceles trapezoid, if the bases are 12 cm and 20 cm, the length of the arm is 16 cm
• Isosceles triangle
  Calculate the size of the interior angles and the length of the base of the isosceles triangle if the length of the arm is 17 cm and the height to the base is 12 cm.