An isosceles triangle has a height of 12.5 m (measured from the unequal side) and two equal angles that measure 55°. Determine the area of the triangle.
Split in half the triangle is a right triangle, so it's three angles are 90%, 55% and 70%.
I'm still not sure how to find the area.
If you split it in half, the three angles are 90, 55, and 35 for one half. You basically find the base of one half of the triangle, multiply it by 2 (to find the base of the full triangle), multiply that by the height and divide it by 2:
tan55=12.5/x
xtan55/tan55=12.5/tan55
x=8.7526 (Rounded)
2x=2(8.7526)=17.5052 (Rounded)
A=bh/2
A=(17.5052)(12.5)/2
A=109.4m^2 (Rounded)
Ah, let me juggle some numbers for you! To find the area of an isosceles triangle, we can use the formula: A = 0.5 * base * height. But since we only have the height, we need to find the base first.
Since we have an isosceles triangle, we know that the two equal angles are each 55°. So, let's use our mathematical clown skills to find the third angle: 180° - 55° - 55° = 70°.
Now, we can use some trigonometry to find the base of the triangle. Let's call it "b". The tangent of the angle 70° is opposite (12.5 m) divided by adjacent (b). So, we have tan(70°) = 12.5 / b.
Now, let me pull out my juggling balls and solve for "b". b = 12.5 / tan(70°). After calculating this, we get a value for the base of the triangle.
Now that we have the base and the height, we can calculate the area using the formula: A = 0.5 * base * height. Just substitute the values we found, and voila! You have the area of the triangle.
I hope my clownish explanation didn't make you juggle too much.
To find the area of an isosceles triangle, you can use the formula:
Area = (base * height) / 2
In this case, the height is given as 12.5 m. However, the base is not given directly. But since the triangle is isosceles and has two equal angles of 55°, we can determine the base by finding the other two angles.
The sum of the three angles in any triangle is always 180°.
Since we know two angles are equal at 55° each, we can subtract the sum of these angles from 180° to find the third angle:
180° - 55° - 55° = 70°
Therefore, we now know that the triangle is a right triangle with angles of 90°, 55°, and 70°.
To find the base, we can use trigonometry. In a right triangle, the tangent of an angle is equal to the length of the opposite side divided by the length of the adjacent side.
In this case, we can use the tangent of the 55° angle to relate it to the base and the height:
tan(55°) = opposite / adjacent
tan(55°) = 12.5 m / base
Now, we can solve for the base by rearranging the formula:
base = 12.5 m / tan(55°)
Using a calculator, we can calculate the value of the tangent of 55° and then divide 12.5 m by that value to find the base.
Calculating the value, we get:
base ≈ 12.5 m / 1.428
base ≈ 8.74 m
Now that we have the base and the height, we can find the area using the formula for the area of a triangle:
Area = (base * height) / 2
Plugging in the values, we get:
Area ≈ (8.74 m * 12.5 m) / 2
Calculating, we find:
Area ≈ 109.25 m²
Therefore, the area of the isosceles triangle is approximately 109.25 square meters.
To find the area of the isosceles triangle, you can use the formula:
Area = (base * height) / 2
In this case, the height of the triangle is given as 12.5 m. However, the base is not directly given.
Since the isosceles triangle has two equal angles measuring 55°, we can infer that the other two angles are also equal, making the triangle an isosceles right triangle. Therefore, the two equal angles are 90° and 55°, while the remaining angle is 180° - (90° + 55°) = 35°.
Since we have a right triangle, we can use trigonometric ratios to find the length of the base. In particular, we can use the tangent ratio:
tan(angle) = opposite / adjacent
In this case, we can use the tangent of 35° to find the length of the base. Let's call the length of the base x.
tan(35°) = 12.5 m / x
We can rearrange this equation to solve for x:
x = 12.5 m / tan(35°)
Now that we have the length of the base, we can substitute it into the area formula:
Area = (base * height) / 2
Area = (x * 12.5 m) / 2
Substituting the value of x we found earlier, the formula becomes:
Area = (12.5 m / tan(35°) * 12.5 m) / 2
Evaluating this expression will give you the area of the isosceles triangle.
If the base is 2x, then
12.5/x = tan 55°
The area is just 12.5x