What is the equation of the line that is perpendicular to the line 5x - 3y = 2 and passes through the point (-1.3)?

A building makes a 90° angle with the ground. A ladder leans against the building, making a 110° exterior angle with the ground.

liberstina [14]

Answer:

A building makes a $90^{\circ}$ angle with the ground .The two interior angles are $70^{\circ}$ and $20^{\circ}$

Solution:

Given, a ladder which is against the building wall makes an exterior angle of $110^{\circ}$

And building makes a $90^{\circ}$ angle with the ground.

So, altogether it makes a right angle triangle with ladder as hypotenuse and ground as base leg and building as another leg.

Now, we know that, sum of exterior angles and interior angles equals to $180^{\circ}$

Here, in the case of ground and ladder, exterior angle is $110^{\circ}$ and interior angle is unknown.

Exterior angle + interior angle = 180

110 + interior angle = 180

Interior angle = 180 – 110

Interior angle = $70^{\circ}$

We have found one of the two interior angles of right angle triangle.

We know that, sum of angles in a triangle is 180 degree

Known Interior angle + unknown interior angle + right angle = 180

70 + unknown interior angle + 90 = 180

Unknown interior angle + 160 = 180

Unknown interior angle = 180 - 160

Unknown interior angle = $20^{\circ}$

Hence the two interior angles are $70^{\circ}$ and $20^{\circ}$

7 0

3 years ago

Find m L M 8.2 100° P 8 7. 29° 13 Q 3 N m 0

Virty [35]

Answer:

bet

Step-by-step explanation:

5 0

2 years ago

B) T is due north of C, calculate the bearing of B from C

choli [55]

Answer:

(a) 52°

(b) 322°

Step-by-step explanation:

(a) The details of the circle are;

The diameter of the circle = AOC

The center of the circle = Point O

The point the line AT cuts the circle = Point B

The point the tangent PT touches the circle = Point C

Angle ∠COB = 76°

We have that angle AOB and angle COB are supplementary angles, therefore;

∠AOB + ∠COB = 180°

∠AOB = 180° - ∠COB

∴ ∠AOB = 180° - 76° = 104°

∠AOB = 104°

OA = OB = The radius of the circle

Therefore, ΔAOB = An isosceles triangle

∠OAB = ∠OBA by base angles of an isosceles triangle are equal

∠AOB + ∠OAB + ∠OBA = 180° by angle summation property

∴ ∠AOB + ∠OAB + ∠OBA = ∠AOB + ∠OAB + ∠OAB = ∠AOB + 2×∠OAB = 180°

∠OAB = (180° - ∠AOB)/2

∴ ∠OAB = (180° - 104°)/2 = 38°

∠TAC = ∠OAB = 38° by reflexive property

AOC is perpendicular to tangent PT at point C, by tangent to a circle property, therefore;

∠TCA = 90° and ΔTCA = A right triangle

∠TAC + ∠ATC + ∠TCA = 180° by angle sum property

∠ATC = 180° - (∠TAC + ∠TCA)

∴ ∠ATC = 180° - (38° + 90°) = 52°

Angle ATC = 52°

(b) In ΔABC, ∠ABC = Angle subtended by the diameter = 90°

∴ ΔABC = A right triangle

∠ABC and ∠TBC are supplementary angles, therefore;

∠ABC + ∠TBC = 180°

∠TBC = 180° - ∠ABC

∴ ∠TBC = 180° - 90° = 90°

∠TCB = 180° - (∠TBC + ∠ATC)

∴ ∠TCB = 180° - (90° + 52°) = 38°

The bearing of B from C = (360° - 38°) = 322°.

7 0

2 years ago

Help please number 7

chubhunter [2.5K]

The answer is D
Hope this helps

6 0

2 years ago

An aquarium at the museum contains 496 gallons of water and is 62% full. How many more gallons are needed to fill up the aquariu

sasho [114]

It will need 188.5 more gallons to be filled

5 0

3 years ago

What is the equation of the line that is perpendicular to the line 5x - 3y = 2 and passes through the point (-1.3)?​

What is the equation of the line that is perpendicular to the line 5x - 3y = 2 and passes through the point (-1.3)?