Following the symbols in the image:
Assuming 15cm corresponds to a (the line adjacent to the angle), then you need to use the cosine formula
cos(ø) = a/h
cos(31º) = 15cm/h
h*cos(31º) = (15cm/h) * h
h*cos(31º) = 15cm * 1
h*cos(31º)/cos(31º) = 15cm/cos(31º)
h*1 = 15cm/cos(31º)
h = 16.398
The length of the third side is 20 cm
We don't know whether the 15cm happens to be the hypotenuse (longest side) of the right triangle. It makes a big difference. -- If the 15cm is the longest side, then the third side is 7.483 cm. (rounded) -- If the 13cm and the 15cm are the "legs", then the hypotenuse is 19.849 cm. (rounded)
Using Pythagoras' theorem: 15 times the square root of 2 cm in length
12 cm
Use Pythagoras' Theorem : In a right angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides. Let H be the hypotenuse then :- H2 = 152 + 82 = 225 + 64 = 289 Then H = √289 = 17cm
The length of the third side is 20 cm
60 cm2
We don't know whether the 15cm happens to be the hypotenuse (longest side) of the right triangle. It makes a big difference. -- If the 15cm is the longest side, then the third side is 7.483 cm. (rounded) -- If the 13cm and the 15cm are the "legs", then the hypotenuse is 19.849 cm. (rounded)
Using Pythagoras' theorem: 15 times the square root of 2 cm in length
Isosceles
12 cm
Use Pythagoras' Theorem : In a right angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides. Let H be the hypotenuse then :- H2 = 152 + 82 = 225 + 64 = 289 Then H = √289 = 17cm
If it's a right angle triangle then by using Pythagoras' theorem the third side is 17 cm
To determine the number of triangles with a perimeter of 15cm, we need to consider the possible side lengths that can form a triangle. The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. With a perimeter of 15cm, the possible side lengths could be (5cm, 5cm, 5cm) for an equilateral triangle, (6cm, 5cm, 4cm) for an isosceles triangle, or (7cm, 5cm, 3cm) for a scalene triangle. Therefore, there are 3 possible triangles that can have a perimeter of 15cm.
To find the area of a triangle, you use the formula: Area = 1/2 * base * height. Plugging in the values, we get Area = 1/2 * 10cm * 15cm = 75 square cm. Therefore, the area of the triangle with a base of 10cm and a height of 15cm is 75 square cm.
Yes
Area = 1/2*9*12 = 54 square cm