Question

To'g'ri burchakli trapetsiyaning otkir burchagi 45 gradusga teng kichik asosi 16 cmga teng trapetsiyaning katta asosini toping

Answer 1

Finding the Length of the Larger Base of a Right Trapezoid with an Opening Angle of 45 Degrees and a Smaller Base of 16 cm

To find the length of the larger base of a right trapezoid with an opening angle of 45 degrees and a smaller base of 16 cm, we can use trigonometric functions to calculate the length of the larger base.

First, let's define the problem: - Opening Angle (θ): 45 degrees - Length of the Smaller Base (a): 16 cm

Calculating the Length of the Larger Base

To calculate the length of the larger base (b) of the trapezoid, we can use the following trigonometric relationship: tan(θ) = (b - a) / (2h)

Where: - θ is the opening angle - a is the length of the smaller base - b is the length of the larger base - h is the height of the trapezoid

We can rearrange the formula to solve for b: b = a + 2h * tan(θ)

Finding the Height of the Trapezoid

To find the height of the trapezoid, we can use the following relationship: h = a * tan(θ/2)

Now, let's substitute the given values into the formulas to find the length of the larger base and the height of the trapezoid.

Calculation

Given: - Opening Angle (θ): 45 degrees - Length of the Smaller Base (a): 16 cm

Using the formula: h = a * tan(θ/2) h = 16 * tan(45/2) h ≈ 16 * tan(22.5) h ≈ 16 * 0.4142 h ≈ 6.628 cm

Now that we have the height of the trapezoid, we can use it to find the length of the larger base: b = a + 2h * tan(θ) b = 16 + 2*6.628 * tan(45) b ≈ 16 + 2*6.628 * 1 b ≈ 16 + 13.256 b ≈ 29.256 cm

Conclusion

The length of the larger base of the right trapezoid with an opening angle of 45 degrees and a smaller base of 16 cm is approximately 29.256 cm.