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Yuri [45]
3 years ago
12

Write the expression in algebraic form. [hint: sketch a right triangle.] tan(arcsec(x/3))

Mathematics
1 answer:
WARRIOR [948]3 years ago
6 0

Sketch  a right triangle having adjacent side(A) is given as “3”, hypotenuse side (H) is “x” and assigning angle “a” as the angle between A and H. Using Pythagorean theorem, you will get “square root of x-squared minus 9” as the opposite side (O). Using SOH CAH TOA function, and since secant is the reciprocal of cosine, sec(a) = x/3. Thus, a = arcsec(x/3). The remaining expression tan(a) is Opposite side over Adjacent side which is equal to “square root of x^2 - 9” over "3". Therefore, the algebraic expression would be: tan(arcsec(x/3)) = “sqrt (x^2 -9)” /3. Different answers can be made depending on which side you consider the “3” and “x”.

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Nicholas drew a triangle with 45, 35, and 100 degree angles. Is there another triangle with the same three angles but different
Anna11 [10]

Answer:

Yes, there are infinite triangles with the same three angles but different side lengths

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

therefore

There are infinite triangles with the same three angles but different side lengths

6 0
3 years ago
If x^(2) - 2 = 2^(2/3) + 2(-2/3) prove that x = 2^(1/3)+2^(-1/3)
dusya [7]

Step-by-step explanation:

x² - 2 = 2^(2/3) + 2^(-2/3)

x² = 2^(2/3) + 2 + 2^(-2/3)

x² = (2^(1/3))² + 2 × 2^(1/3) × 2^(-1/3) +

(2^(-1/3))² (It is in the form of a²+2ab+b²)

x² = (2^(1/3) + 2^(-1/3))²

x = 2^(1/3) + 2^(-1/3)

6 0
3 years ago
Help me what is X/5-3/7
yaroslaw [1]

Answer:

15/7 or 2.142

Step-by-step explanation:

x=3/7×5

x=15/7

3 0
3 years ago
Find the area of the shaded triangle
Ivanshal [37]

Answer:

18 square units

Step-by-step explanation:

The square shows you the width and height of the triangle.

The area of any triangle if equal to 0.5 * width * height, so:

0.5 * 6 * 6 = 3 * 6 = 18 square units.

6 0
2 years ago
A rectangle field has an area of 300 square meters and a perimeter of 80 meters. what are the length and width of the field?
Yakvenalex [24]
By definition the area of a rectangle is:
 A = w * l
 The perimeter is:
 P = 2w + 2l
 Where,
 w: width
 l: long
 Substituting values:
 300 = w * l
 80 = 2w + 2l
 Solving the system of equations we have:
 l = 30 m
 w = 10 m
 Answer:
 
The length and width of the field are:
 
l = 30 m
 
w = 10 m
6 0
3 years ago
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