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Alenkasestr [34]
3 years ago
8

Triangle 1 has an angle that measures 62° and an angle that measures 14°. Triangle 2 has an angle that measures 14° and an angle

that measures x°, where x ≠ 62º. Based on the information, Bob claims that triangle 1 and triangle 2 cannot be similar.
2. What value of x, in degrees, will refute Bob’s claim?
Mathematics
1 answer:
Lapatulllka [165]3 years ago
6 0

Answer:

<u>If x ≠ 62° and we want to Refute Bob's claim that  Δ1 and  Δ2 cannot be similar, the value of x should be:</u>

<u>x = 104°</u>

Step-by-step explanation:

<u>Let's recall that the interior angles of a triangle add up to 180°, therefore:</u>

Δ 1 = ∠62° + ∠14° + ∠180° - (62° + 14°)

Δ 1 = ∠62° + ∠14° + ∠104°

Then,

Δ 2 = ∠x° + ∠14° + ∠180° - (x° + 14°)

Δ 2 = ∠x° + ∠14° + ∠166° - x°

<u>If x ≠ 62° and we want to Refute Bob's claim that  Δ1 and  Δ2 cannot be similar, the value of x should be:</u>

x = 104°

<u>Replacing with x = 104, in  Δ 2 = ∠x° + ∠14° + ∠166° - x°:</u>

Δ 2 = ∠104° + ∠14° + ∠166° - 104°

Δ 2 = ∠104° + ∠14° + ∠62°

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In the △ABC, the height AN = 24 in, BN = 18 in, AC = 40 in. Find AB and BC.
strojnjashka [21]

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AB = 30 inch

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Step-by-step explanation:

Make a drawing. Please see the attachment. All measurements are in inches.

Consider the two triangles:

∆ ABC and ∆ AB'C

1. Looking only at ∆ ABC. Since this is <em>not</em> a rectangular triangle, let's first consider ∆ ANC, so we can calculate NC.

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We want to calculate NC, so:

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AN is the height and there fore is perpendicular to B'C. Let's consider ∆ AB'N, so we can calculate AB'.

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Extra:

Please look at the picture again, but now concentrate on the indicated 50 and - 50...

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minus value of your calculated outcome.

Not always, but <em>usually</em> there is some sort of meaning to the negative part of the SQRT, you just need to be willing to understand what it possibly could mean.

I hope this has made some sense to you :-).

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