An isosceles triangle ABC has two sides 17cm in length and a base 10cm in length. Find the size of the angle between the equal sides.
Draw the altitude to the base. Then, if the angle is x,
sin(x/2) = 5/17
now you know x/2, so just double it.
To find the size of the angle between the equal sides of an isosceles triangle, we can use the following steps:
Step 1: Draw the triangle and label the sides and angles. In this case, we have an isosceles triangle ABC with two equal sides (17 cm each) and a base (10 cm).
Step 2: Recall that in an isosceles triangle, the angles opposite the equal sides are equal. Let's call this angle x.
Step 3: Use the fact that the sum of the angles in a triangle is 180 degrees. In our triangle, we have 1 angle x and 2 angles equal to y (the base angles).
Step 4: Set up an equation to solve for x. We know that x + y + y = 180.
Step 5: Simplify the equation by combining like terms. x + 2y = 180.
Step 6: Since we have another piece of information (the base), we can use it to find y. Recall that the base angles of an isosceles triangle are equal. Therefore, we can use the equation 2y + x = 180.
Step 7: Substitute the value of x in terms of y from the previous equation into this equation. We get 2y + (x in terms of y) = 180.
Step 8: Substitute the value of x in terms of y into the equation x + 2y = 180. We get (x in terms of y) + 2y = 180.
Step 9: Solve the equation for y. This will help us find the value of the base angles.
Step 10: Once we have found y, substitute it back into the equation (x in terms of y) + 2y = 180 to find the value of x.
Following the steps above, we can find the size of the angle between the equal sides of the isosceles triangle ABC with sides 17 cm, 17 cm, and a base of length 10 cm.