If the hypotenuse of a right triangle is 10 units and angle B is 70 degrees determine angle A and the other sides of the triangle.
- print Print
- list Cite
Expert Answers
calendarEducator since 2008
write3,662 answers
starTop subjects are Math, Science, and Social Sciences
Given the triangle ABC such that:
B = 70 degrees.
Then The other angles are:
A = 90 degrees.
C = 20 degrees.
Then the hypotenuse is BC = 10 units.
Now we will calculate the length of the legs.
==> AC = BC*cos B = 10*cos70 = 10*0.3420 = 3.42 units
==> AB = BC*cos C = 10*cos20 = 10*0.9397 = 9.367 units.
Then the angles of the triangle are:
A = 90 degrees
B = 70 degrees.
C = 20 degrees.
The length of the sides are:
AB = 9.367 units.
BC = 10 units.
AC = 3.42 units.
Related Questions
- A right angle triangle has a 40 degree angle and hypotenuse = 10. Find the other angles and sides.
- 1 Educator Answer
- GeometryIf the hypotenuse of a right triangle is 10 units and angle B is 70 degrees determine...
- 1 Educator Answer
- Right angle triangle.A right angle triangle has a 40 degree angle and hypotenuse = 10. Find the...
- 1 Educator Answer
- ABC is a right angle triangle. AB = 10 A = 27 degree. Find BC if AC is the hypotenuse.
- 2 Educator Answers
- A right triangle has a perimeter of 24 cm and a hypotenuse of 10 cm. Find the sides x and y, x...
- 2 Educator Answers
calendarEducator since 2010
write12,551 answers
starTop subjects are Math, Science, and Business
We have a right angled triangle and one of the sides given as 70 degrees. Now the second side is 180 - 90 - 70 = 20 degrees.
Also, the hypotenuse is 10. Let the other sides be a and b.
So cos 70 = a / 10 =.3420
a = .3420*10 = 3.420
cos 20 = b/ 10 = .9396
b = 0.9396*10 = 9.396
Therefore the sides of the triangle are 10, 3.42 and 9.396. The angles of the triangle are 90, 70 and 20 degrees.
Let's suppose that the right angle is A = 90 degrees. The hypotenuse is opposite side to the right angle.
That means that B+C = 70 + C = 90
C = 90 - 70
C = 20 and B = 70
To determine the lengths of the other cathetus, we'll apply the Pythagorean theorem and the sine function.
The sine function is a ratio between the opposite cathetus and the hypothenuse. We'll note the cathetus as x and y.
sin B = x/10
sin 70 = x/10
x = 10*sin 70
x = 10*0.93
x = 9.4 units
We'll apply Pythagorean theorem in a right angle triangle:
10^2 = x^2 + y^2
100 = 88.36 + y^2
y^2 = 100 - 88.36
y^2 = 11.64
y = 3.4 units
We'll keep only the positive value for y, since it is the length of the cathetus of the right angle triangle and it cannot be negative.
Student Answers