Use the image to answer the question.
An illustration shows two triangles, one big and one small. In the small triangle, one side measures 11.4 inches and another side measures 18 inches. In the big triangle, the side corresponding to 11.4 inches in the small triangle measures x and the side corresponding to 18 inches measures 23.4 inches.
What is the length of x in decimal form to the nearest hundredth?
(1 point)
To find the length of x, we can set up a proportion using the equal ratios of corresponding sides in similar triangles:
11.4 inches / 18 inches = x / 23.4 inches
Cross-multiplying, we get:
11.4 inches * 23.4 inches = 18 inches * x
266.76 inches = 18x
Dividing both sides by 18, we find:
x = 14.82 inches
Therefore, the length of x in decimal form to the nearest hundredth is 14.82 inches.
△XYZ∼△RST. m∠X=50°, m∠S=79°. What is the measure of angle T?(1 point)
To find the measure of angle T, we can use the fact that corresponding angles in similar triangles are congruent.
Since ∠X corresponds to ∠S, we have:
m∠X = m∠S
Therefore, the measure of angle T is 50°.
Given △ABC∼△DEF, m∠A=52°, and m∠E=11°, what is the measure of angle C?(1 point)
To find the measure of angle C, we can use the fact that corresponding angles in similar triangles are congruent.
Since ∠A corresponds to ∠E, we have:
m∠A = m∠E
Substituting the given values, we have:
52° = 11°
However, this is not possible since 52° is not equal to 11°. Therefore, we cannot determine the measure of angle C with the given information.
To find the length of x, we need to find the corresponding side in the big triangle. Using the concept of similarity, we can set up a proportion between the sides of the two triangles:
Small triangle: Side 1 = 11.4 inches, Side 2 = 18 inches
Big triangle: Side 1 = x inches, Side 2 = 23.4 inches
We can set up the proportion as follows:
11.4/18 = x/23.4
To solve for x, we can cross multiply and then divide:
11.4 * 23.4 = 18 * x
265.56 = 18 * x
Now, divide both sides of the equation by 18 to solve for x:
x = 265.56/18
x ≈ 14.753
Therefore, the length of x, to the nearest hundredth, is approximately 14.75 inches.
To find the length of x in the big triangle, we can use the concept of similar triangles. Similar triangles have corresponding angles that are equal and corresponding sides that are proportional.
In the given illustration, the small triangle is similar to the big triangle. This means that the ratio of corresponding sides in the two triangles is equal.
We can set up a proportion using the given information:
11.4 inches / 18 inches = x / 23.4 inches
To solve for x, we can cross multiply and then divide:
11.4 inches * 23.4 inches = 18 inches * x
266.76 square inches = 18 inches * x
To isolate x, we divide both sides by 18 inches:
(266.76 square inches) / (18 inches) = x
x ≈ 14.82 inches
Therefore, the length of x is approximately 14.82 inches (to the nearest hundredth).