All categories

3 years ago

Given: Tangents LA and LB m∠AOB=110° Find: m∠ALO.

Mathematics

1 answer:

Ad libitum [116K]3 years ago

7 0

Answer:

35°

Step-by-step explanation:

From any point outside a circle, the two tangents to that circle are always congruent to each other. This can be proven by taking the two triangles ΔLAO and ΔLBO and prove that they are congruent. From the upper triangle AO is congruent to BO because AO = BO = Radius. Also, LO is the same length for both triangles, therefore two equal sides. Moreover, the measure of an angle between the tangent to a point of the circle and the radius going from the center to that point equals 90°, so ∠LAO = ∠LBO = 90°. So these two triangles ΔLAO and ΔLBO are congruent by SSA postulate.

If m∠AOB=110°, then m∠AOL = 110°/2 =55°. Finally, the angles of every triangle always measures 180°, therefore:

m∠ALO = 180°-55°-90 = 35°

You might be interested in

5+ 1/5x=5 what is x

Alenkasestr [34]

Answer:

x = 0

Step-by-step explanation:

Solve for x:

x/5 + 5 = 5

Put each term in x/5 + 5 over the common denominator 5: x/5 + 5 = x/5 + 25/5:

x/5 + 25/5 = 5

x/5 + 25/5 = (x + 25)/5:

(x + 25)/5 = 5

Multiply both sides of (x + 25)/5 = 5 by 5:

(5 (x + 25))/5 = 5×5

(5 (x + 25))/5 = 5/5×(x + 25) = x + 25:

x + 25 = 5×5

5×5 = 25:

x + 25 = 25

Subtract 25 from both sides:

x + (25 - 25) = 25 - 25

25 - 25 = 0:

x = 25 - 25

25 - 25 = 0:

Answer: x = 0

4 0

3 years ago

Read 2 more answers

Mercury is a naturally occurring metal that can be harmful to humans. The current recommendation is for humans to take in no mor

kirill [66]

Answer:

A.) A person weights 80 kg can consume Haddock fish = 149 grams

B.) A person weights 80 kg can consume Swordfish fish = 8 grams

C.) A person weights 80 kg can consume Tuna fish = 23 grams

D.) A person weights 80 kg can consume Snapper fish = 50 grams

Step-by-step explanation:

Given - Mercury is a naturally occurring metal that can be harmful to humans. The current recommendation is for humans to take in no more than 0.1 microgram for every kilogram of their weight per day. Fish generally carry high levels of mercury, although certain fish have higher mercury content than others. Fish, however, are healthy sources of many other nutrients, so nutritionists recommend keeping them in the human diet. The figure below shows the average mercury content of several types of fish.

To find - If a person weighs 82 kg, how much of each fish can they safely consume? round to the nearest gram.

A.Haddock

B.Swordfish

C.Tuna

D.Snapper

Proof -

Firstly, determine how many micro grams of mercury a person can consume who weighs 82 kilograms.

⇒82 × 0.1 = 8.2 micro grams.

Now,

a.)

For Haddock fish-

It consumes 0.055 micro grams of mercury

So,

A person can consume fish = 8.2 ÷ 0.055

= 149.09 ≈ 149 grams

So,

A person weights 80 kg can consume Haddock fish = 149 grams

b.)

For Swordfish fish-

It consumes 0.995 micro grams of mercury

So,

A person can consume fish = 8.2 ÷ 0.995

= 8.24 ≈ 8 grams

So,

A person weights 80 kg can consume Swordfish fish = 8 grams

c.)

For Tuna fish-

It consumes 0.350 micro grams of mercury

So,

A person can consume fish = 8.2 ÷ 0.350

= 23.43 ≈ 23 grams

So,

A person weights 80 kg can consume Tuna fish = 23 grams

d.)

For Snapper fish-

It consumes 0.165 micro grams of mercury

So,

A person can consume fish = 8.2 ÷ 0.165

= 49.697 ≈ 50 grams

So,

A person weights 80 kg can consume Snapper fish = 50 grams

6 0

3 years ago

Point c has the coordinate -7 and d has the coordinate 6 on a number line. What is the distance between c and d

OLga [1]

Answer:

Step-by-step explanation:

7 0

3 years ago

To change knots per hour, use the expression 1.15k, where k is the speed in in knots per hour. A plane is flying at 300 knots pe

Free_Kalibri [48]

1.15(300).
Substitute k for 300, since the plane is flying 300 knots per hour, and k=knots per hour.

1.15(300)=345 miles per hour
After multiplying, 300 by 1.15, you get 345 miles per hour. This is the speed of the plane from Knots to MPH (Miles Per Hour).

8 0

3 years ago

Read 2 more answers

3 On a coordinate grid, the location of a lighthouse is at L, and the location of a buoy is at B. At noon, a ship is at the midp

Zarrin [17]

Answer:

$(\frac{1}{2}, 2)$

Step-by-step explanation:

Using the midpoint formula, $M(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$ , we can find the coordinates that represents the position of the ship at noon.