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3 years ago

Need some assistance lovely’s

Mathematics

2 answers:

liraira [26]3 years ago

7 0

Answer:

Step-by-step explanation:

sum of measure of interior angles of a triangle is 180

x+x+x=180

3x=180

x=180/3

x=60

Sladkaya [172]3 years ago

3 0

Answer:

Step-by-step explanation:

The sum of the angles of a triangle is 180

x+x+x = 180

3x= 180

Divide by 3

3x/3=180/3

x = 60

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Find the exact values of the remaining five trigonometric functions of theta, suppose theta is an angle in the standard position

nexus9112 [7]

Answer:

$\sin(\theta)=60/61\text{ and } \csc(\theta)=61/60\\\cos(\theta)=11/61\text{ and } \sec(\theta)=61/11\\\tan(\theta)=60/11\text{ and } \cot(\theta)=11/60$

Step-by-step explanation:

So, we know that:

$\tan(\theta)=60/11\text{ and } 90\textdegree$

Since θ is in QI, this means that all of our trig ratios will be positive. Recall All Students Take Calculus. Since it's QI, we refer to A in All. The A tells us that all the ratios will be positive.

Now, let's figure out the remaining ratios knowing that all of them is positive. First, let's find the hypotenuse. Recall that tangent is the ratio of the opposite side to the adjacent side. So, we can use the Pythagorean Theorem to find the hypotenuse. So:

$a^2+b^2=c^2$

Substitute 60 for a and 11 for b:

$60^2+11^2=c^2$

Solve for c. Square both numbers:

$3600+121=c^2$

Add:

$c^2=3721$

Take the square root of both sides:

$c=61$

Therefore, the hypotenuse is 61.

So, our side lengths are: Opposite=60; Adjacent=11; and Hypotenuse=61.

Now that we know the lengths, we can find the other trig ratios:

Sine and Cosecant:

$\sin(\theta)=opp/hyp$

Substitute 60 for Opp and 61 for Hyp:

$\sin(\theta)=60/61$

Cosecant is the reciprocal of sine. So:

$\csc(\theta)=61/60$

Cosine and Secant:

$\cos(\theta)=adj/hyp$

Substitute 11 for Adj and 61 for Hyp:

$\cos(\theta)=11/61$

Secant is the reciprocal of cosine. So:

$\sec(\theta)=61/11$

Tangent and Cotangent:

We are already given that tangent is:

$\tan(\theta)=60/11$

Cotangent is the reciprocal of tangent. So:

$\cot(\theta)=11/60$

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How to find it is related to the opposite angle in a cyclic quadrilateral is equal to 180 degeres

lorasvet [3.4K]

Answer: The measure of ∠BEF=110°.

Step-by-step explanation:

Given: In cyclic quadrilateral ABCD, ∠C = 110°

Then, ∠A+∠C=180° [The sum of opposite angles in a cyclic quadrilateral is 180 degrees.]

⇒ ∠A+ 110°=180°

⇒ ∠A = 180° - 110°

⇒ ∠A = 70°

In cyclic quadrilateral ABEF,

∠A+∠E=180° [The sum of opposite angles in a cyclic quadrilateral is 180 degrees.]

⇒ 70° + ∠E=180°

⇒∠E=110°

Hence, the measure of ∠BEF=110°.

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Korolek [52]

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