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3 years ago

State if the triangles are similar. If so, how do you know they are similar and complete the similarity statement.

Mathematics

1 answer:

timofeeve [1]3 years ago

3 0

Answer:

YES by SAS

triangle TUV is similar to triangle TLM

Step-by-step explanation:

The ratios of the sides

24/6 = 4

36/9 = 4

so the sides are similar

We know angle UTV = angle LTM because they are vertical angles

we have side included angle side

The triangles are similar by SAS ( side angle side)

triangle TUV is similar to triangle TLM

You might be interested in

If f(x) = x2 − 2x + 9 and g(x) = 8 − x, what is (f o g)(−4)? A. 111 B. 144 C. 120 D. 129

lapo4ka [179]

Answer: OPTION D

Step-by-step explanation:

Given the functions $f(x) = x^2 - 2x + 9$ and $g(x) = 8 - x$ , you need to substitute the function g(x) into the function f(x), then:

$(fog)(x)=(8-x)^2 - 2(8-x) + 9$

Now, you need substitute the input value $x=-4$ into $(fog)(x)$ , then you get the following output value:

$(fog)(-4)=(8-(-4))^2 - 2(8-(-4)) + 9$

$(fog)(x)=(8+4)^2 - 2(8+4) + 9$

$(fog)(x)=(12)^2 - 2(12) + 9$

$(fog)(x)=129$

This matchis with the option D

6 0

4 years ago

Angle (theta) is in standard position. If (8,-15) is on the terminal ray of angle (theta), find the values of the trigonometric

mariarad [96]

Answer:

$\sin \theta =\frac{-15}{17}\\cos \theta =\frac{8}{17}\\\tan \theta =\frac{-15}{8}\\\csc \theta =\frac{-17}{15}\\\sec \theta =\frac{17}{8}\\\cot \theta =\frac{-8}{15}$

Step-by-step explanation:

Given: (8,-15) is on the terminal ray of angle

To find: All the trigonometric ratios

Solution:

Trigonometry is a branch of mathematics that explain relationship between the sides and angles of triangles.

If (x, y) lies on the terminal side of θ then $r=\sqrt{x^2+y^2}$

$r=\sqrt{(8)^2+(-15)^2}=\sqrt{64+225}=\sqrt{289}=17$ units

$\sin \theta =\frac{y}{r}=\frac{-15}{17}\\cos \theta =\frac{x}{r}=\frac{8}{17}\\\tan \theta =\frac{y}{x}=\frac{-15}{8}\\\csc \theta =\frac{1}{\sin \theta }=\frac{-17}{15}\\\sec \theta =\frac{1}{cos \theta}=\frac{17}{8}\\\cot \theta =\frac{1}{\tan \theta}=\frac{-8}{15}$